John Mann, who became the first Labour backbencher to call for him to go on Saturday, hailed it as a "wise and brave" decision.
He said the party now needed to "regroup" to fight the Tories in Opposition.
Slough MP Fiona Mactaggart, who has criticised Mr Brown's leadership in the past, said he had done the "right thing".
"It is a recognition that Labour lost the election, which I think has not been made clear until this point," she told a radio programme.
"I understand that the constitutional position is that he remains Prime Minister and that's an issue so he needed to stay on in that role. I don't know why it took him until today to say that he felt that there should be a new future leader of the Labour Party. It's a hard decision to make."
Mr Mann (Bassetlaw) denied there would be any "rejoicing" in the party.
"We've just lost the election. We've a minority Tory government that wants to make public sector cuts that we need to fight against. That's why we needed a new leader to regroup and take on this Tory onslaught on our public services.
"It is the right decision. It allows us to move forward. But we've just lost an election. We need to get real."
Sir Stuart Bell (Middlesbrough) said Mr Brown had offered a "viable alternative" to the Tory party. Labour and the Liberal Democrats were closer on the economy and would avoid the kind of cuts the Tories were threatening. "Gordon has been very wise, very sensible and very courageous," he said.