Collaborative and Other Relationships Collaborative and Other Relationships - Collaborations (Details) - USD ($) shares in Millions, $ in Millions	1 Months Ended	3 Months Ended				9 Months Ended
	Jan. 31, 2019	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Sep. 30, 2017	Dec. 31, 2018	Sep. 30, 2018	Sep. 30, 2017	Jun. 05, 2018
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Research and development		$ 507.9			$ 446.4		$ 1,985.6	$ 1,666.0
Inventory charges		460.8			370.0		1,327.8	1,120.8
Total revenues		3,439.0			3,077.8		9,926.6	8,966.9
Collaboration profit (loss) sharing		47.5			35.2		129.2	82.5
ZINBRYTA
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Research and development				$ 12.8
Inventory charges				$ 2.4
Total revenues		0.0			14.2		1.4	41.0
OCREVUS
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Royalty operating profit threshold for highest royalty rate percentage							$ 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]
Total revenues		511.7			406.5		$ 1,445.3	1,144.2
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
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 | BAN2401 and Elenbecestat
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Expense incurred by the collaboration		64.9			38.3		$ 176.0	105.0
Expense reflected within statements of income		32.5			19.2		88.0	52.5
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]
Total 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		0.2			0.7		2.0	2.0
Rest of world | ZINBRYTA
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Total revenues		0.0			14.2		$ 1.4	41.0
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		64.8			73.3		204.8	202.2
Expense reflected within statements of income		55.1			73.3		183.6	202.2
Selling, general and administrative | Eisai | Aducanumab
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Expense incurred by the collaboration		12.1			5.1		33.3	14.9
Expense reflected within statements of income		5.1			5.1		19.0	14.9
AbbVie | Collaborative arrangement
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Total revenues		(0.7)			(2.8)		(7.9)	(12.6)
AbbVie | U.S. | Collaborative arrangement
Collaborative Arrangements and Non-collaborative Arrangement Transactions [Line Items]
Total revenues		(0.7)			(2.8)		(7.9)	(12.6)
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		358.0			325.1		1,066.6	996.1
Other revenues from anti-CD20 therapeutic programs		$ 153.7			$ 81.4		$ 378.7	$ 148.1