The vote in the Commons was much less close than the referendum vote.
MPs have voted by a majority of 384 to allow Prime Minister Theresa May to get Brexit negotiations under way.
They backed the government’s European Union Bill, supported by the Labour leadership, by 498 votes to 114.
But the SNP, Plaid Cymru and the Liberal Democrats opposed the bill, while 47 Labour MPs and Tory ex-chancellor Ken Clarke rebelled.
The bill now faces further scrutiny in the Commons and the House of Lords before it can become law.
The prime minister has set a deadline of 31 March for invoking Article 50 of the Lisbon Treaty, getting official talks with the EU started. The bill returns to the Commons next week.