Equity Reclassification out of Accumulated Other Comprehensive Income (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	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Reclassification Adjustment out of Accumulated Other Comprehensive Income on Derivatives [Line Items]
Nonoperating Income (Expense)									$ 83.3	$ 11.0	$ (217.0)
Income tax benefit (expense)									1,158.0	1,425.6	2,458.7
Product Revenues	$ 3,671.3	$ 3,600.1	$ 3,616.7	$ 3,489.8	$ 3,526.3	$ 3,439.0	$ 3,356.5	$ 3,131.1	14,377.9	13,452.9	12,273.9
Net income attributable to Biogen Inc.	$ 1,439.7	$ 1,545.9	$ 1,494.1	$ 1,408.8	$ 946.8	$ 1,444.4	$ 866.6	$ 1,172.9	5,888.5	4,430.7	2,539.1
Reclassification out of Accumulated Other Comprehensive Income
Reclassification Adjustment out of Accumulated Other Comprehensive Income on Derivatives [Line Items]
Net income attributable to Biogen Inc.									125.6	(47.0)	(44.2)
Unrealized Gains (Losses) on Securities Available for Sale | Reclassification out of Accumulated Other Comprehensive Income
Reclassification Adjustment out of Accumulated Other Comprehensive Income on Derivatives [Line Items]
Nonoperating Income (Expense)									4.5	(8.5)	(19.5)
Income tax benefit (expense)									(0.9)	1.8	6.8
Unrealized Gains (Losses) on Cash Flow Hedges | Reclassification out of Accumulated Other Comprehensive Income
Reclassification Adjustment out of Accumulated Other Comprehensive Income on Derivatives [Line Items]
Nonoperating Income (Expense)									0.3	0.3	0.3
Income tax benefit (expense)									(0.6)	0.2	0.1
Product Revenues									118.6	(42.5)	(32.5)
Operating Expenses									(3.3)	(0.2)	(0.6)
Gains (Losses) on Net Investment Hedge | Reclassification out of Accumulated Other Comprehensive Income
Reclassification Adjustment out of Accumulated Other Comprehensive Income on Derivatives [Line Items]
Nonoperating Income (Expense)									$ 7.0	$ 1.5	$ 0.0