Intangible Assets and Goodwill (Details) - USD ($) $ in Millions	3 Months Ended				6 Months Ended		12 Months Ended
	Jun. 30, 2017	Mar. 31, 2017	Dec. 31, 2016	Jun. 30, 2016	Jun. 30, 2017	Jun. 30, 2016	Dec. 31, 2016
Intangible assets
Amortization of acquired intangible assets	$ 117.5			$ 92.9	$ 566.0	$ 181.7
Total intangible assets, gross	8,218.3		$ 7,742.3		8,218.3		$ 7,742.3
Accumulated Amortization	(4,167.0)		(3,934.0)		(4,167.0)		(3,934.0)
Intangible assets, net	4,051.3		3,808.3		4,051.3		3,808.3
Payment made to Forward Pharma					1,250.0
TECFIDERA intellectual property charges							454.8
Intangible Assets and Goodwill (Textual) [Abstract]
Accumulated impairment losses related to goodwill	0.0				0.0
Expected future amortization expense, 2017 (remaining six months)	222.6				222.6
Expected future amortization expense, 2018	425.8				425.8
Expected future amortization expense, 2019	412.5				412.5
Expected future amortization expense, 2020	378.6				378.6
Expected future amortization expense, 2021	239.3				239.3
Expected future amortization expense, 2022	216.7				216.7
TECFIDERA
Intangible assets
Amortization of acquired intangible assets	29.4				383.0
Increase in acquired and in-licensed rights and patents		$ 795.2
Out-licensed patents
Intangible assets
Cost	543.3		543.3		543.3		543.3
Accumulated Amortization	(529.8)		(523.6)		(529.8)		(523.6)
Net	13.5		19.7		$ 13.5		19.7
Out-licensed patents | Minimum
Intangible assets
Estimated life, (in years)					13 years
Out-licensed patents | Maximum
Intangible assets
Estimated life, (in years)					23 years
Developed technology
Intangible assets
Cost	3,005.3		3,005.3		$ 3,005.3		3,005.3
Accumulated Amortization	(2,662.2)		(2,634.3)		(2,662.2)		(2,634.3)
Net	343.1		371.0		$ 343.1		371.0
Developed technology | Minimum
Intangible assets
Estimated life, (in years)					15 years
Developed technology | Maximum
Intangible assets
Estimated life, (in years)					23 years
Developed technology | AVONEX
Intangible assets
Net	335.9				$ 335.9
Acquired and in-licensed rights and patents
Intangible assets
Cost	3,937.1		3,481.7		3,937.1		3,481.7
Accumulated Amortization	(975.0)		(776.1)		(975.0)		(776.1)
Net	2,962.1		2,705.6		$ 2,962.1		2,705.6
Acquired and in-licensed rights and patents | Minimum
Intangible assets
Estimated life, (in years)					4 years
Acquired and in-licensed rights and patents | Maximum
Intangible assets
Estimated life, (in years)					18 years
Acquired and in-licensed rights and patents | SPINRAZA
Intangible assets
Increase in acquired and in-licensed rights and patents			60.0		$ 50.0
In Process Research and Development [Member]
Intangible assets
Indefinite lived intangible assets useful life					Indefinite until commercialization
Cost and Net	668.6		648.0		$ 668.6		648.0
Accumulated Amortization	0.0		0.0		$ 0.0		0.0
Trademarks and Trade Names [Member]
Intangible assets
Indefinite lived intangible assets useful life					Indefinite
Cost and Net	64.0		64.0		$ 64.0		64.0
Accumulated Amortization	0.0		$ 0.0		0.0		$ 0.0
TYSABRI product | Acquired and in-licensed rights and patents
Intangible assets
Net	$ 2,351.8				$ 2,351.8