Collaborative and Other Relationships - Collaborations (Details) $ in Millions	1 Months Ended				3 Months Ended					6 Months Ended		9 Months Ended
	Apr. 30, 2022 USD ($)	Aug. 31, 2021 USD ($)	Jun. 30, 2021 USD ($)	Dec. 31, 2019 product	Sep. 30, 2022 USD ($)	Mar. 31, 2022 USD ($)	Dec. 31, 2021 USD ($)	Sep. 30, 2021 USD ($)	Mar. 31, 2020 USD ($)	Jun. 30, 2023 USD ($)	Jun. 30, 2022 USD ($)	Sep. 30, 2022 USD ($)	Sep. 30, 2021 USD ($)
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Percentage of future development costs related to Eisai												45.00%
Research and Development Expense (Excluding Acquired in Process Cost)					$ 549.2			$ 702.4				$ 1,629.5	$ 1,801.7
Cost of sales, excluding amortization and impairment of acquired intangible assets					469.5			511.8				1,707.4	1,449.6
(Gain) loss on equity method investments												2.6	17.2
Samsung Bioepis
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
(Gain) loss on equity method investments								8.9				17.0	39.5
Loss recorded on Samsung Bioepis joint venture								1.1				2.6	17.2
Amortization								$ 7.8				14.4	22.3
ADUHELM
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Research and development expense												300.0
Cost of sales, excluding amortization and impairment of acquired intangible assets						$ 275.0
ADUHELM | Maximum | Forecast
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Research and development expense										$ 335.0
Eisai
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Percentage of future development costs related to Eisai								45.00%
(Gain) loss on equity method investments					3.4			$ 50.6				214.0	90.7
Due from Related Parties					110.6		$ 285.4					110.6
Due to Related Parties					81.7		46.5					81.7
Eisai | BAN2401 and Elenbecestat
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Expense Incurred By Collaboration					109.3			118.4				264.9	236.1
Expense reflected within statements of income					54.7			59.2				132.5	118.0
Eisai | ADUHELM
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Expense reflected within statements of income					0.0			0.0				0.0	45.0
Additional milestone payment			$ 100.0		0.0			0.0				0.0	100.0
(Gain) loss on equity method investments						$ 59.0	45.0	45.0				$ 177.0
Samsung Bioepis
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Upfront and milestone payments made to collaborative partner									$ 100.0
Collaboration agreement term												5 years
Research and development expense									$ 63.0
Additional milestone payment	$ 50.0
Due from Related Parties					1.8		4.1					$ 1.8
Due to Related Parties					53.8		$ 148.7					$ 53.8
Contingent Commercialized Rights, Number Of Products | product				2
Sangamo Therapeutics, Inc. Agreement
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Term of collaboration agreement												5 years
Other research and discovery
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Research and Development Expense (Excluding Acquired in Process Cost)					14.0			7.7				$ 51.5	84.9
InnoCare Pharma Limited (InnoCare) Agreement
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Upfront and milestone payments made to collaborative partner		$ 125.0
Contingent additional milestone payment		$ 812.5
Research and development | Eisai | ADUHELM
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Expense incurred by the collaboration					34.6			43.7				116.0	132.8
Expense reflected within statements of income					19.0			24.0				63.8	73.0
Research and development | Denali Therapeutics
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Expense incurred by the collaboration					19.9			8.5				58.0	27.2
Expense reflected within statements of income					11.4			5.1				33.5	16.3
Research and development | Samsung Bioepis
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Expense incurred by the collaboration					5.5			6.2			$ 16.4	16.4
Expense reflected within statements of income					3.1			1.9			$ 9.5	10.2
Research and development | Sage Therapeutics Inc.
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Expense incurred by the collaboration					40.9			40.8				130.4	134.9
Expense reflected within statements of income					20.5			20.4				65.2	67.3
Research and development | UCB Pharma S.A. [Member]
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Expense incurred by the collaboration					18.3			16.5				51.5	49.5
Expense reflected within statements of income					9.1			8.2				25.7	24.8
Selling, general and administrative | Eisai | BAN2401 and Elenbecestat
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Expense incurred by the collaboration					29.0			5.6				68.3	15.6
Expense reflected within statements of income					14.5			2.8				34.2	7.8
Selling, general and administrative | Eisai | ADUHELM
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Expense incurred by the collaboration					(8.0)			154.3				127.8	391.7
Expense reflected within statements of income					(3.9)			83.3				68.1	211.2
Selling, general and administrative | Sage Therapeutics Inc.
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Expense incurred by the collaboration					28.5			7.4				69.9	23.2
Expense reflected within statements of income					$ 14.2			$ 3.7				$ 34.9	$ 11.6