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Intangible Assets and Goodwill (Details) - USD ($)
$ in Millions
3 Months Ended 12 Months Ended
Dec. 31, 2019
Sep. 30, 2019
Jun. 30, 2019
Mar. 31, 2019
Dec. 31, 2018
Sep. 30, 2018
Jun. 30, 2018
Mar. 31, 2018
Mar. 31, 2017
Dec. 31, 2019
Dec. 31, 2018
Dec. 31, 2017
Jun. 07, 2019
Intangible assets                          
Cost $ 7,379.3       $ 7,187.3         $ 7,379.3 $ 7,187.3    
Total intangible assets, gross 8,408.8       7,727.3         8,408.8 7,727.3    
Accumulated Amortization (4,881.4)       (4,607.3)         (4,881.4) (4,607.3)    
Net 2,497.9       2,580.0         2,497.9 2,580.0    
Intangible assets, net 3,527.4       3,120.0         3,527.4 3,120.0    
Amortization and impairment of acquired intangible assets                   489.9 747.3 $ 814.7  
Amortization of acquired intangible assets                   274.0 381.2 455.3  
Contingent Consideration (2.6) $ 57.8 $ 20.0 $ (11.5) (79.3) $ 87.9 $ (1.9) $ 5.6   63.7 12.3 $ (62.7)  
Intangible Assets and Goodwill (Additional Textual)                          
Expected future amortization expense, 2020 260.0                 260.0      
Expected future amortization expense, 2021 220.0                 220.0      
Expected future amortization expense, 2022 225.0                 225.0      
Expected future amortization expense, 2023 230.0                 230.0      
Expected future amortization expense, 2024 220.0                 220.0      
Increase to goodwill                   $ 117.5 1,080.1    
Payment made to Forward Pharma                 $ 1,250.0        
Minimum                          
Intangible assets                          
Estimated life, (In Years)                   4 years      
Maximum                          
Intangible assets                          
Estimated life, (In Years)                   28 years      
In-process research and development                          
Intangible assets                          
Indefinite lived intangible assets useful life                   Indefinite      
Cost and net 965.5       476.0         $ 965.5 476.0    
Accumulated Amortization 0.0       0.0         $ 0.0 0.0    
Impairment of IPR&D   215.9       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    
TYSABRI                          
Intangible assets                          
Net 1,800.0                 1,800.0      
VUMERITY                          
Intangible assets                          
Net change in acquired and in-licensed rights and patents 155.0                        
TECFIDERA                          
Intangible assets                          
Net $ 36.1               795.2 $ 36.1      
Impairment of in-licensed patent         $ 176.8       $ 328.2        
BG00011                          
Intangible assets                          
Contingent Consideration   $ 61.2                      
PLSR | In-process research and development                          
Intangible assets                          
Amortization of acquired intangible assets           60.0              
TGN | In-process research and development                          
Intangible assets                          
Cost and net           41.8              
Amortization of acquired intangible assets           $ 129.3              
Nightstar                          
Intangible assets                          
In-process research and development                         $ 700.0