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Intangible Assets and Goodwill (Details) - USD ($)
$ in Millions
3 Months Ended 12 Months Ended
Dec. 31, 2018
Sep. 30, 2018
Dec. 31, 2017
Mar. 31, 2017
Dec. 31, 2016
Dec. 31, 2018
Dec. 31, 2017
Dec. 31, 2016
Finite-Lived Intangible Assets [Line Items]                
Amortization and impairment of acquired intangible assets           $ 747.3 $ 814.7 $ 385.6
Increase to goodwill           1,080.1 1,267.3  
Intangible assets                
Total intangible assets, gross $ 7,727.3   $ 8,264.6     7,727.3 8,264.6  
Accumulated Amortization (4,607.3)   (4,385.0)     (4,607.3) (4,385.0)  
Intangible assets, net 3,120.0   3,879.6     3,120.0 3,879.6  
Intangible Assets and Goodwill (Additional Textual)                
Expected future amortization expense, 2019 270.0         270.0    
Expected future amortization expense, 2020 290.0         290.0    
Expected future amortization expense, 2021 250.0         250.0    
Expected future amortization expense, 2022 250.0         250.0    
Expected future amortization expense, 2023 230.0         230.0    
Amortization of acquired intangible assets           381.2 455.3 373.4
Impairment of out-licensed patent               12.2
Contingent Consideration           12.3 (62.7) (14.8)
Payment made to Forward Pharma       $ 1,250.0        
TECFIDERA litigation settlement charge         $ 454.8 0.0 0.0 $ 454.8
Out-licensed patents                
Intangible assets                
Cost 543.3   543.3     543.3 543.3  
Accumulated Amortization (542.3)   (535.6)     (542.3) (535.6)  
Net 1.0   7.7     $ 1.0 7.7  
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 (2,734.8)   (2,689.0)     (2,734.8) (2,689.0)  
Net 270.5   316.3     $ 270.5 316.3  
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 3,638.7   3,971.4     $ 3,638.7 3,971.4  
Accumulated Amortization (1,330.2)   (1,160.4)     (1,330.2) (1,160.4)  
Net 2,308.5   2,811.0     $ 2,308.5 2,811.0  
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 476.0   680.6     $ 476.0 680.6  
Accumulated Amortization 0.0   0.0     $ 0.0 0.0  
Intangible Assets and Goodwill (Additional Textual)                
Amortization of acquired intangible assets   $ 189.3            
Impairment of out-licensed patent   189.3            
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 265.0         265.0    
TYSABRI | Acquired and in-licensed rights and patents                
Intangible assets                
Net 2,027.1         2,027.1    
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 176.8     328.2        
Impairment of out-licensed patent 176.8     328.2        
TECFIDERA | Acquired and in-licensed rights and patents                
Intangible assets                
Net 71.0     795.2   $ 71.0    
Intangible Assets and Goodwill (Additional Textual)                
Amortization of acquired intangible assets 176.8     $ 328.2        
PLSR | In-process research and development                
Intangible Assets and Goodwill (Additional Textual)                
Amortization of acquired intangible assets   60.0            
TGN                
Intangible Assets and Goodwill (Additional Textual)                
Contingent Consideration $ 80.6 89.6            
TGN | In-process research and development                
Intangible assets                
Cost and net   41.8            
Intangible Assets and Goodwill (Additional Textual)                
Amortization of acquired intangible assets   $ 129.3