The former foreign secretary, who had faced private calls to clarify his position within the party, will resign immediately to allow him to take up what the Mirror described as his "dream job" as chief executive of the global charity. His decision will trigger a byelection in South Shields, where he has been MP since 2001.
Lord Mandelson, the former business secretary led tributes to the "huge" contribution Miliband has made but said it would be wrong to write off his future in British politics.
Mandelson told the World Tonight on Radio 4: "He just combined policy, good judgment, real concern, a knowledge of economics and an ability to tie things together. That is how he will be remembered. And that is why he why he will be a loss. But never say never. I wouldn't say goodbye to David Miliband forever in British politics."
Friends of Miliband told the Guardian he had decided to abandon British politics to end the "permanent pantomime" over his political relationship with his younger brother Ed who narrowly beat him to the Labour leadership in 2010.
One friend said: "David was always clear that it was time for him to make a decision this year about his future. The feeling was that if he came back into the shadow cabinet it would be a permanent pantomime. But equally if he did not come back, but remained in the PLP [parliamentary Labour party], it would also be a permanent pantomime. It was therefore not sustainable."
Miliband had indicated that he would continue serving as an MP after losing the Labour leadership to his brother, Ed, in 2010. But he has felt for some time that he needed to make a decision on whether he could remain in the frontline of British politics
One friend said: "We are facing an election that Labour can win. We need to remove anything that can get in the way of that. David owed it to Ed and to the Labour party to put an end to the endless speculation. He has made that call and shown what a big figure he is. It is very sad but he has done this in the best interests of the party."
The former foreign secretary, whose wife Louise is an American violinist, has decided instead to embark on a completely different career by working for the International Rescue Committee (IRC) which provides emergency relief to victims of conflict.
Miliband's successor as foreign secretary, William Hague, visited a displacement camp for victims of rape run by the IRC with Angelina Jolie in the eastern Democratic Republic of Congo this week.
Jack Straw, Miliband's predecessor but one as foreign secretary, paid a warm tribute to him. Straw told the World Tonight: "His abilities were legion. He has got a very very sharp mind. He is very good at developing personal relationships. He is trusted and he made a big difference, particularly in that last three years of a Labour government under Gordon Brown, in helping to secure Britain's exit from Iraq, in winding down our responsbilities in Afghanistan and also helping to rebalance the British government's position in the world following all the traumas after 9/11 and our relationship with the Americans. So it is a very very big legacy."
Straw added that all members of the parliamentary Labour party would be sorry. "This is hard. He has made this decision and I respect him for it although all of us in the PLP and in the wider Labour movement will be very sorry to see him go though we understand exactly why he has felt he had to make that decision.
Straw agreed with Mandelson that Miliband may have a future in British politics. "I agree with Peter Mandelson. These days exiting from the house of commons at one stage – he is only 47 – is not the end of his political life at all. He may feel after running the IRC that he wants to come back into British politics and he will be welcomed back into the Labour movement if he does want to come back."
Straw said Ed Miliband would have mixed feelings. "I can't be inside in the relationship between Ed Miliband and his older brother David … But I guess that Ed will both be relieved that a decision has been made for him about what to do with David but also very sorry to see such a talent leave and what could have been a great partnership not be there for the immediate future."
David Lammy, the former minister, tweeted: "David Miliband a big loss to PLP. Will miss him. Very loyal friend. The right decision however for him Louise and his two boys. Great new job."
Tim Farron, the president of the Lib Dems, tweeted: "If this story is true, it's a big loss for parliament … David was a big thinker, great politician and a lovely man."
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