Stock-Based Compensation - Summary of Incentive Equity Awards (Details) - $ / shares	12 Months Ended
Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2019
Stock Options
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]
Beginning balance (in shares)	3,770,787	4,201,614	4,478,288
Granted (in shares)	359,464	501,192	528,978
Exercised (in shares)	(756,915)	(905,231)	(784,372)
Expired/forfeited (in shares)	(169,654)	(26,788)	(21,280)
Ending balance (in shares)	3,203,682	3,770,787	4,201,614
Weighted Average Exercise Price
Beginning balance (in dollars per share)	$ 74.97	$ 63.85	$ 55.69
Granted (in dollars per share)	147.97	117.43	98.72
Exercised (in dollars per share)	46.26	46.47	39.94
Expired/forfeited (in dollars per share)	105.40	88.01	94.14
Ending balance (in dollars per share)	$ 88.33	$ 74.97	$ 63.85
Time-based RSUs
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]
Beginning balance of RSUs (in shares)	699,998	819,299	982,399
Granted RSUs (in shares)	382,340	340,006	360,147
Vesting of RSUs (in shares)	(272,131)	(408,716)	(430,270)
Expired/forfeited RSUs (in shares)	(48,870)	(50,591)	(92,977)
Ending balance of RSUs (in shares)	761,337	699,998	819,299
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value [Roll Forward]
Beginning balance (in dollars per share)	$ 111.37	$ 92.15	$ 67.72
Granted (in dollars per share)	132.21	118.74	121.11
Vesting of RSUs (in dollars per share)	122.92	78.76	63.97
Expired/forfeited (in dollars per share)	121.32	113.07	76.57
Ending balance (in dollars per share)	$ 117.07	$ 111.37	$ 92.15
Performance-based RSUs
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]
Beginning balance of RSUs (in shares)	251,596	325,777	395,689
Granted RSUs (in shares)	141,838	110,260	133,213
Vesting of RSUs (in shares)	(122,146)	(176,900)	(198,420)
Expired/forfeited RSUs (in shares)	(23,708)	(7,541)	(4,705)
Ending balance of RSUs (in shares)	247,580	251,596	325,777
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value [Roll Forward]
Beginning balance (in dollars per share)	$ 122.11	$ 97.43	$ 74.29
Granted (in dollars per share)	126.96	120.09	116.53
Vesting of RSUs (in dollars per share)	119.15	77.19	64.50
Expired/forfeited (in dollars per share)	122.76	80.24	80.57
Ending balance (in dollars per share)	$ 126.29	$ 122.11	$ 97.43

Share-Based Compensation Arrangement By Share-Based Payment Award, Equity Instruments Other Than Options, Vested

No definition available.

Name:	br_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVested
Namespace Prefix:	br_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

The number of equity-based payment instruments, excluding stock (or unit) options, that were forfeited during the reporting period.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average fair value as of the grant date of equity-based award plans other than stock (unit) option plans that were not exercised or put into effect as a result of the occurrence of a terminating event.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

The number of grants made during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

The weighted average fair value at grant date for nonvested equity-based awards issued during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Per share or unit weighted-average fair value of nonvested award under share-based payment arrangement. Excludes share and unit options.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

The weighted average fair value as of grant date pertaining to an equity-based award plan other than a stock (or unit) option plan for which the grantee gained the right during the reporting period, by satisfying service and performance requirements, to receive or retain shares or units, other instruments, or cash in accordance with the terms of the arrangement.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of equity instruments other than options outstanding, including both vested and non-vested instruments.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

For presentations that combine terminations, the number of shares under options that were cancelled during the reporting period as a result of occurrence of a terminating event specified in contractual agreements pertaining to the stock option plan or that expired.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average price of options that were either forfeited or expired.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Gross number of share options (or share units) granted during the period.

+ References

No definition available.

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of options outstanding, including both vested and non-vested options.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(i)-(ii)
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average price at which grantees can acquire the shares reserved for issuance under the stock option plan.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- References

No definition available.

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average price at which option holders acquired shares when converting their stock options into shares.

+ References

No definition available.

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average per share amount at which grantees can acquire shares of common stock by exercise of options.

+ References

No definition available.

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of share options (or share units) exercised during the current period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)(2)
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-URI http://asc.fasb.org/extlink&oid=120397183&loc=d3e187085-122770

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(28))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=123467817&loc=d3e21463-112644

+ Details

Name:	us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_AwardTypeAxis=us-gaap_EmployeeStockOptionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=br_TimeBasedRestrictedStockMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=br_PerformanceBasedRestrictedStockUnitsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: