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Equity (Details Textual) - USD ($)
shares in Millions, $ in Millions
3 Months Ended 9 Months Ended
Sep. 30, 2018
Sep. 30, 2017
Sep. 30, 2018
Sep. 30, 2017
Jan. 01, 2018
Sep. 30, 2016
Mar. 31, 2011
Class of Stock [Line Items]              
Payments for repurchase of common stock     $ 3,000.0 $ 1,365.4      
Equity increase during the period     1,200.0        
Net income attributable to Biogen Inc. $ 1,444.4 $ 1,226.1 3,483.9 $ 2,836.5      
2018 Share Repurchase Program [Member]              
Class of Stock [Line Items]              
Authorized amount of share repurchases under the 2016 Share Repurchase Program $ 3,500.0   $ 3,500.0        
2016 Share Repurchase Program              
Class of Stock [Line Items]              
Authorized amount of share repurchases under the 2016 Share Repurchase Program           $ 5,000.0  
Repurchase and retire of common stock, shares     10.5 3.7      
Payments for repurchase of common stock     $ 3,000.0 $ 1,000.0      
2011 Share Repurchase Program              
Class of Stock [Line Items]              
Common stock shares authorized for repurchased             20.0
Repurchase of common stock, shares       1.2      
Payments for repurchase of common stock       $ 365.4      
Accounting Standards Update 2016-16 | Retained earnings              
Class of Stock [Line Items]              
Cumulative effect of new accounting principle         $ 500.0