Britain will get to decide on 5 May whether the "first past the post" system for electing MPs should be reformed after Peers gave in to the House of Commons in a late-night battle of wills.
Earlier in the evening, Peers had defied the Commons to insist that the outcome of the referendum should be binding only if the turnout was at least 40 per cent.
But their vote was reversed by MPs, who voted by 310 votes to 231 (a majority of 79) to overturn the measure for a second time.
The vote then returned to the Lords, who backed down in the face of the prospect of an all-night sitting. Second time round, Labour's amendment was defeated by 68 votes.
The result means that the the Parliamentary Voting System and Constituencies Bill will be on the statute book by next week – the minimum time necessary for to prepare for the referendum on introducing the alternative-vote system to be held in May.
The result will be a relief for both Nick Clegg and David Cameron, who have suffered weeks of uncertainty over the legislation which formed a key part of the coalition agreement.
In a sometimes heated debate in both Houses, Conservative rebels argued that the bill should be amended to allow Parliament to reverse the referendum result if there was not a significant turnout.
In the early evening, Peers voted by 277 to 215 in favour of the call by the former Labour minister Lord Rooker to impose the 40 per cent threshold.
His amendment received heavyweight backing from six former Tory ministers – Lord Lawson of Blaby, Lord Lamont of Lerwick, Lord Forsyth of Drumlean, Lord Howe of Aberavon, Lord Tebbit and Lord Mawhinney.