The bill was approved by 494 votes to 122, and now moves to the House of Lords.
Shadow business secretary Clive Lewis was one of 52 Labour lawmakers to defy party orders to back the bill and he resigned from the front bench.
PM Theresa May wants to trigger formal Brexit talks by the end of March.
The prime minister will do this by invoking Article 50 of the Lisbon Treaty, but requires Parliament’s permission before doing so.
Clive Lewis, who earlier said he was undecided on whether to support the EU (Notification of Withdrawal) Bill, announced his resignation as parliament began voting for the final time.
He said he “cannot, in all good conscience, vote for something I believe will ultimately harm the city I have the honor to represent, love and call home”.
Leader Jeremy Corbyn said he understood the difficulties the vote presented some of his members of parliament but said they had been ordered to back the Article 50 because the party would not “block Brexit”.
Shadow home secretary Diane Abbott, who missed last week’s initial vote on the bill, backed it this time.
The Labour rebellion was five lawmakers up on last week’s vote, while former Chancellor Ken Clarke was again the only Conservative to vote against the two-clause bill.
During the voting, SNP lawmakers were reprimanded by deputy speaker Lindsay Hoyle after they started singing Ode to Joy, the EU anthem.
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