Intangible Assets and Goodwill (Details) - USD ($) $ in Millions	3 Months Ended					12 Months Ended
	Dec. 31, 2017	Sep. 30, 2017	Jun. 30, 2017	Mar. 31, 2017	Dec. 31, 2016	Dec. 31, 2017	Dec. 31, 2016	Dec. 31, 2015
Intangible assets
Total intangible assets, gross	$ 8,264.6				$ 7,742.3	$ 8,264.6	$ 7,742.3
Accumulated Amortization	(4,385.0)				(3,934.0)	(4,385.0)	(3,934.0)
Intangible assets, net	3,879.6				3,808.3	3,879.6	3,808.3
Intangible Assets and Goodwill (Additional Textual)
Expected future amortization expense, 2018	423.5					423.5
Expected future amortization expense, 2019	401.8					401.8
Expected future amortization expense, 2020	381.6					381.6
Expected future amortization expense, 2021	254.3					254.3
Expected future amortization expense, 2022	242.3					242.3
Amortization of acquired intangible assets						(814.7)	(385.6)	$ (382.6)
Payment made to Forward Pharma				$ 1,250.0
TECFIDERA litigation settlement charge					454.8	0.0	454.8	$ 0.0
Out-licensed patents
Intangible assets
Cost	543.3				543.3	543.3	543.3
Accumulated Amortization	(535.6)				(523.6)	(535.6)	(523.6)
Net	7.7				19.7	$ 7.7	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	(2,689.0)				(2,634.3)	(2,689.0)	(2,634.3)
Net	316.3				371.0	$ 316.3	371.0
Developed technology | Minimum
Intangible assets
Estimated life, (In Years)						15 years
Developed technology | Maximum
Intangible assets
Estimated life, (In Years)						23 years
Acquired and in-licensed rights and patents
Intangible assets
Cost	3,971.4				3,481.7	$ 3,971.4	3,481.7
Accumulated Amortization	(1,160.4)				(776.1)	(1,160.4)	(776.1)
Net	2,811.0				2,705.6	$ 2,811.0	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
In-process research and development
Intangible assets
Indefinite lived intangible assets useful life						Indefinite
Cost and net	680.6				648.0	$ 680.6	648.0
Accumulated Amortization	0.0				0.0	$ 0.0	0.0
Trademarks and trade names
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
AVONEX | Developed technology
Intangible assets
Net	309.5					309.5
TYSABRI | Acquired and in-licensed rights and patents
Intangible assets
Net	2,236.2					2,236.2
SPINRAZA | Acquired and in-licensed rights and patents
Intangible Assets and Goodwill (Additional Textual)
Net change in acquired and in-licensed rights and patents						90.0
Biosimilars | Acquired and in-licensed rights and patents
Intangible Assets and Goodwill (Additional Textual)
Net change in acquired and in-licensed rights and patents						25.0	$ 50.0
ZINBRYTA
Intangible Assets and Goodwill (Additional Textual)
Impairment of out-licensed patent	31.2
TECFIDERA
Intangible Assets and Goodwill (Additional Textual)
Amortization of acquired intangible assets	$ (30.8)	$ (30.4)	$ (29.4)	(353.6)		$ (444.2)
Net change in acquired and in-licensed rights and patents				$ 795.2