Intangible Assets and Goodwill (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2019	Mar. 31, 2018	Dec. 31, 2018
Intangible assets
Total intangible assets, gross	$ 7,731.8		$ 7,727.3
Accumulated Amortization	(4,675.6)		(4,607.3)
Intangible assets, net	3,056.2		3,120.0
Amortization and impairment of acquired intangible assets	68.2	$ 103.9
Intangible Assets and Goodwill (Textual) [Abstract]
Accumulated impairment losses related to goodwill	0.0
Expected future amortization expense, 2019 (remaining nine months)	200.0
Expected future amortization expense, 2020	290.0
Expected future amortization expense, 2021	250.0
Expected future amortization expense, 2022	250.0
Expected future amortization expense, 2023	230.0
Expected future amortization expense, 2024	190.0
Out-licensed patents
Intangible assets
Cost	543.3		543.3
Net	0.9		1.0
Accumulated Amortization	$ (542.4)		(542.3)
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
Net	261.2		270.5
Accumulated Amortization	$ (2,744.1)		(2,734.8)
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	$ 256.2
Acquired and in-licensed rights and patents
Intangible assets
Cost	3,638.7		3,638.7
Net	2,249.6		2,308.5
Accumulated Amortization	$ (1,389.1)		(1,330.2)
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 | TYSABRI
Intangible assets
Net	$ 1,980.8
Acquired and in-licensed rights and patents | TECFIDERA
Intangible assets
Net	$ 63.1
In Process Research and Development
Intangible assets
Indefinite lived intangible assets useful life	Indefinite until commercialization
Cost and Net	$ 480.5		476.0
Accumulated Amortization	$ 0.0		0.0
Trademarks and Trade Names
Intangible assets
Indefinite lived intangible assets useful life	Indefinite
Cost and Net	$ 64.0		64.0
Accumulated Amortization	$ 0.0		$ 0.0