Other Comprehensive Income and Accumulated Other Comprehensive Income (Changes in AOCI) (Details) - USD ($) $ in Millions	3 Months Ended	9 Months Ended
Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2020	Sep. 30, 2019
Accumulated Other Comprehensive Income (Loss) [Roll Forward]
Beginning Balance			$ (66.8)	$ (9.7)
Other comprehensive income (loss) before reclassifications			(60.3)	(7.9)
Amounts reclassified from other comprehensive income			7.9	(30.6)
Other comprehensive (loss) income, net of tax	$ (8.3)	$ 9.7	(52.4)	(38.5)
Ending Balance	(119.2)	(48.2)	(119.2)	(48.2)
Defined Benefit Pension Plans
Accumulated Other Comprehensive Income (Loss) [Roll Forward]
Beginning Balance			(9.2)	(2.6)
Other comprehensive income (loss) before reclassifications			0.0	0.0
Amounts reclassified from other comprehensive income			0.0	0.0
Other comprehensive (loss) income, net of tax			0.0	0.0
Ending Balance	(9.2)	(2.6)	(9.2)	(2.6)
Unrealized Gains (Losses) from Debt Securities
Accumulated Other Comprehensive Income (Loss) [Roll Forward]
Beginning Balance			(0.1)	(0.3)
Other comprehensive income (loss) before reclassifications			0.1	0.2
Amounts reclassified from other comprehensive income			0.0	0.0
Other comprehensive (loss) income, net of tax			0.1	0.2
Ending Balance	0.0	(0.1)	0.0	(0.1)
Unrealized Gains (Losses) from Hedging Activities
Accumulated Other Comprehensive Income (Loss) [Roll Forward]
Beginning Balance			(40.1)	9.6
Other comprehensive income (loss) before reclassifications			(55.1)	(5.1)
Amounts reclassified from other comprehensive income			7.9	(30.6)
Other comprehensive (loss) income, net of tax			(47.2)	(35.7)
Ending Balance	(87.3)	(26.1)	(87.3)	(26.1)
Foreign Currency Translation Adjustment
Accumulated Other Comprehensive Income (Loss) [Roll Forward]
Beginning Balance			(17.4)	(16.4)
Other comprehensive income (loss) before reclassifications			(5.3)	(3.0)
Amounts reclassified from other comprehensive income			0.0	0.0
Other comprehensive (loss) income, net of tax			(5.3)	(3.0)
Ending Balance	$ (22.7)	$ (19.4)	$ (22.7)	$ (19.4)

Accumulated Other Comprehensive Income (Loss) [Roll Forward]

No definition available.

Name:	alxn_AccumulatedOtherComprehensiveIncomeLossRollForward
Namespace Prefix:	alxn_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Accumulated change in equity from transactions and other events and circumstances from non-owner sources, net of tax effect, at period end. Excludes Net Income (Loss), and accumulated changes in equity from transactions resulting from investments by owners and distributions to owners. Includes foreign currency translation items, certain pension adjustments, unrealized gains and losses on certain investments in debt and equity securities, other than temporary impairment (OTTI) losses related to factors other than credit losses on available-for-sale and held-to-maturity debt securities that an entity does not intend to sell and it is not more likely than not that the entity will be required to sell before recovery of the amortized cost basis, as well as changes in the fair value of derivatives related to the effective portion of a designated cash flow hedge.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 11
-URI http://asc.fasb.org/extlink&oid=118930883&loc=d3e637-108580

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 14A
-URI http://asc.fasb.org/extlink&oid=118930883&loc=SL7669686-108580

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 14
-URI http://asc.fasb.org/extlink&oid=118930883&loc=d3e681-108580

+ Details

Name:	us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount after tax, before reclassification adjustments of other comprehensive income (loss).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 14A
-URI http://asc.fasb.org/extlink&oid=118930883&loc=SL7669686-108580

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 55
-Paragraph 15
-URI http://asc.fasb.org/extlink&oid=118951672&loc=d3e1436-108581

+ Details

Name:	us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount after tax of other comprehensive income (loss) attributable to parent entity.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 1B
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=118930883&loc=SL7669625-108580

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 810
-SubTopic 10
-Section 50
-Paragraph 1A
-Subparagraph (c)(3)
-URI http://asc.fasb.org/extlink&oid=109239629&loc=SL4573702-111684

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 810
-SubTopic 10
-Section 45
-Paragraph 20
-URI http://asc.fasb.org/extlink&oid=108774443&loc=SL4569643-111683

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 1A
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=118930883&loc=SL7669619-108580

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 810
-SubTopic 10
-Section 45
-Paragraph 19
-URI http://asc.fasb.org/extlink&oid=108774443&loc=SL4569616-111683

+ Details

Name:	us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount after tax of reclassification adjustments of other comprehensive income (loss).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 17B
-URI http://asc.fasb.org/extlink&oid=118930883&loc=SL34724394-108580

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 14A
-URI http://asc.fasb.org/extlink&oid=118930883&loc=SL7669686-108580

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 55
-Paragraph 15
-URI http://asc.fasb.org/extlink&oid=118951672&loc=d3e1436-108581

+ Details

Name:	us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_AccumulatedDefinedBenefitPlansAdjustmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_AccumulatedTranslationAdjustmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: