They voted 351 to 32, majority 319, for the so-called Weatherill amendment on the fourth day of committee debate on the House of Lords Bill.
Lord Irvine of Lairg, the Lord Chancellor, said he would expect "no unreasonable obstruction" of the legislation during its remaining passage through Parliament in return for the Government's support for the amendment.
"It is the most significant amendment to the Bill, significant because it represents an inspired way forward by consensus towards a major constitutional change. We know it is a compromise and none the worse for that.
"It doesn't give perfect satisfaction to my party. It is not a complete fulfilment of our manifesto commitment on which the Government is entitled to insist.
"But the best compromises often don't give complete satisfaction to everyone. That is the nature of a compromise," he told peers during the Bill's resumed committee stage.
He also dismissed as "fanciful and without foundation" speculation that Lords reform would not move beyond stage one, which will abolish hereditaries' voting rights, pledging the Government's determination to press ahead with reform of the second chamber.
The amendment put forward by Lord Weatherill, the chairman of the crossbenchers, caused the sacking of Viscount Cranborne as Opposition peers' leader last year after it emerged that he helped to negotiate the deal without the knowledge of William Hague.
Lord Strathclyde, the new Tory Lords leader, urged his backbenchers to support the amendment because it gave the Government an incentive to move on with reform and avoided the "nightmare of a wholly appointed House". But, at a briefing earlier, Lord Strathclyde admitted his party was split over the amendment and some Tory peers would seek to increase the 92 to more.
He also indicated his party would challenge the Government on how the hereditaries would be elected if stage one of reform lasted for longer than envisaged and any of the original 92 died.
During his speech, he added: "We are still being compelled forcibly forward on a journey to an undeclared destination. The train rattles forward and behind us the wrecker gangs move in to jemmy up the railway tracks, leaving nothing in their place."
Lord Rodgers of Quarrybank, the Liberal Democrat Leader in the Lords, said his party would not vote against the "dog's breakfast" amendment. "It is wrong in principle because it perpetuates the hereditary principle."
Lord Richard, the former Labour leader of the Lords, said the amendment served "purely as a matter of convenience" for the parties involved. "As far as I am concerned it makes a good Bill a bit worse."Reuse content