Collaborative and Other Relationships Collaborative and Other Relationships - Collaborations (Details) - USD ($) shares in Millions, $ in Millions	1 Months Ended	3 Months Ended			6 Months Ended		9 Months Ended
	Jan. 31, 2019	Jun. 30, 2018	Mar. 31, 2018	Jun. 30, 2017	Jun. 30, 2018	Jun. 30, 2017	Dec. 31, 2018	Jun. 05, 2018
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Research and development		$ 981.0		$ 796.2	$ 1,477.7	$ 1,219.6
Inventory charges		421.0		366.2	867.0	750.8
Other revenues		(3,356.5)		(3,078.4)	(6,487.6)	(5,889.1)
Collaboration profit (loss) sharing		39.2		26.5	81.7	47.3
ZINBRYTA
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Research and development			$ 12.8
Inventory charges			$ 2.4
Other revenues		0.0		(16.1)	(1.4)	(26.8)
OCREVUS
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Royalty operating profit threshold for highest royalty rate percentage		900.0			$ 900.0
Reduction in royalty rate					50.00%
Period of collaboration agreement					11 years
Revenues from anti-CD20 therapeutic programs
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Other revenues		$ (490.4)		(397.1)	$ (933.6)	(737.7)
Ionis Pharmaceuticals
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Term of collaboration agreement		10 years
Total payment to enter collaboration agreement								$ 1,000.0
Upfront payment for collaboration agreement								$ 375.0
Investment in common stock, shares purchased								11.5
Purchase of common stock								$ 625.0
Prepaid research and development services		$ 50.9			$ 50.9
Research and development		324.1
Investment in common stock, value								462.9
Premium on purchase of common stock								$ 162.1
AbbVie
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Biogen share of co-promotion profits or losses					50.00%
Eisai | E2609 and BAN2401
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Expense incurred by the collaboration		54.6		29.5	$ 111.1	66.7
Expense reflected within statements of income		27.3		14.7	55.5	33.3
Genentech
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Collaboration expenses in dispute					120.0
Reimbursement of aducanumab | Eisai
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Percentage of future development costs related to Eisai	45.00%						15.00%
U.S. | ZINBRYTA
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Other revenues		0.0		0.0	0.0	0.0
E.U. and Canada | AbbVie
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Collaboration profit (loss) sharing		0.5			1.8	1.3
Rest of world | ZINBRYTA
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Other revenues		0.0		(16.1)	$ (1.4)	(26.8)
Rest of world | OCREVUS
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Royalties percentage to be received on sale of product					3.00%
Minimum | OCREVUS
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Royalties percentage to be received on sale of product					13.50%
Minimum | Ionis Pharmaceuticals
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Estimated additional payments upon achievement of milestones					$ 125.0
Maximum | OCREVUS
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Royalties percentage to be received on sale of product					24.00%
Maximum | Ionis Pharmaceuticals
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Estimated additional payments upon achievement of milestones					$ 270.0
Research and development | Eisai | Aducanumab
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Expense incurred by the collaboration		76.5		74.6	140.0	128.9
Expense reflected within statements of income		65.0		74.6	128.5	128.9
Selling, general and administrative | Eisai | Aducanumab
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Expense incurred by the collaboration		14.0		4.8	21.2	9.8
Expense reflected within statements of income		9.2		4.8	13.9	9.8
AbbVie | Collaborative arrangement
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Other revenues		(2.5)		(3.9)	(7.2)	(9.8)
AbbVie | U.S. | Collaborative arrangement
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Other revenues		(2.5)		(3.9)	(7.2)	(9.8)
Genentech
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Biogen's share of pre-tax profits in the U.S. for RITUXAN and GAZYVA, including the reimbursement of selling and development expenses		359.0		347.5	708.6	671.0
Other revenues from anti-CD20 therapeutic programs		$ 131.4		$ 49.6	$ 225.0	$ 66.7