The concession avoided a rebellion in May's ruling Conservative party over a bill empowering the prime minister to start formal exit negotiations, a move she has promised to make by the end of March.
The government warned however that if parliament rejected the terms of the final deal, including any agreement on a new trading relationship with the EU, Britain would still leave the bloc.
"This will be a meaningful vote. It will be a choice between leaving the European Union with a negotiated deal or not," Brexit minister David Jones told the House of Commons.
However, she refused to accept an amendment that would have enshrined this concession into law, and this evening, MPs rejected it by 326 votes to 293.
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Seven members of May's Conservative party rebelled - fewer than expected.
The two-clause bill now looks likely to clear the Commons without too much trouble at the end of its debate stage tomorrow, when it will head to the House of Lords to be approved by peers.
Some MPs had argued that parliament should be able to vote against the deal obtained by the government, and force ministers to seek a better one.
But Jones rejected this idea, warning: "To send the government back to the negotiating table would be the surest way of undermining our negotiating position and delivering a worse deal."
He also noted that Britain would need the agreement of the other 27 EU member states to extend the two-year timetable.