Lord Mandelson cannot take up some of the most senior government posts
Life peers are to be given the right to resign from the House of Lords - something hereditary peers have been able to do since 1963.
The measure will be included in a Constitutional Reform Bill, due to go before Parliament on Monday.
The bill will also bring an end to the hereditary principle.
The changes would mean peers, such as Lord Mandelson, would be free to give up titles, stand as MPs and possibly take up more senior government posts.
Although Lord Mandelson is the government's first secretary, the jobs of foreign secretary, chancellor of the exchequer or prime minister would pose constitutional difficulties for an unelected peer.
Asked last month by the Financial Times whether he might renounce his peerage and stand again as an MP, Lord Mandelson said: "It's not legally possible to do that. I am trapped. I believe it is for life."
The peer, who insisted he was "teasing", added: "Of course, you could always change the law."
MPs voted in 2007 for an 80% or 100% elected upper house - something that Gordon Brown has indicated will feature in Labour's general election manifesto.
At the moment all peers are appointed, apart from the 92 hereditaries, who survived the first phase of Lords reform during Tony Blair's first term as prime minister.
Government sources have said the Constitutional Reform Bill will tackle some of this unfinished Lords reform business.
For example, by-elections are currently used for replacing hereditary peers when one of their number dies, keeping their numbers topped up.
The bill would scrap that device, so the number of hereditary peers in the House of Lords would gradually dwindle to none.