Accumulated Other Comprehensive Income (Loss) (Details 1) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2017	Sep. 30, 2017	Jun. 30, 2017	Mar. 31, 2017	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Other income (expense)									$ (10.5)	$ (14.7)	$ (18.3)
Income tax benefit (expense)									1,425.6	2,458.7	1,237.3
Revenues	$ (3,526.3)	$ (3,439.0)	$ (3,356.5)	$ (3,131.1)	$ (3,307.0)	$ (3,077.8)	$ (3,078.4)	$ (2,810.7)	(13,452.9)	(12,273.9)	(11,448.8)
Nonoperating Income (Expense)									11.0	(217.0)	(218.7)
Net income attributable to Biogen Inc.	$ 946.8	$ 1,444.4	$ 866.6	$ 1,172.9	$ (297.4)	$ 1,226.1	$ 862.8	$ 747.6	4,430.7	2,539.1	3,702.8
Reclassification out of Accumulated Other Comprehensive Income [Member]
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Net income attributable to Biogen Inc.									(47.0)	(44.2)	3.4
Unrealized Gains (Losses) on Securities Available for Sale | Reclassification out of Accumulated Other Comprehensive Income [Member]
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Other income (expense)									(8.5)	(19.5)	(0.9)
Income tax benefit (expense)									1.8	6.8	0.3
Accumulated Gain (Loss), Net, Cash Flow Hedge, Parent [Member] | Reclassification out of Accumulated Other Comprehensive Income [Member]
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Revenues									(42.5)	(32.5)	5.3
Unrealized Gains (Losses) on Cash Flow Hedges | Reclassification out of Accumulated Other Comprehensive Income [Member]
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Income tax benefit (expense)									0.2	0.1	0.0
Operating Expenses									0.2	0.6	(1.5)
Nonoperating Income (Expense)									0.3	0.3	0.2
Gains (losses) on net investment hedge | Reclassification out of Accumulated Other Comprehensive Income [Member]
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Income tax benefit (expense)									0.0	0.0	0.0
Nonoperating Income (Expense)									$ 1.5	$ 0.0	$ 0.0