The bill was passed with 494 votes to 122, without a single amendment.
It will now be sent to the House of Lords, where Labour and Liberal Democrat peers are expected to press for concessions on issues including the status of EU citizens in the UK.
The bill’s clearance by the House of Commons is a success for Theresa May, who appears to be on track with her pledge to trigger article 50 by the end of March.
Clive Lewis, MP for Norwich South, has resigned as shadow business secretary.
He was among 52 Labour MPs to rebel against Corbyn’s three-line whip and vote against the bill.