He will leave the role next month after he fulfils “outstanding commitments”, a source close to Mr Blair told the BBC.
Mr Blair, who took the role just hours after leaving Downing Street in 2007, has written to UN Secretary General Ban Ki-Moon to confirm his decision.
He will “remain active” in the region in an informal role, the source said.
Mr Blair remains “fully committed to assisting the international community in its work with Israel and the Palestinians to bring about progress on the two-state solution”, they said.
“He believes that he can best support these efforts through working with the key regional players, the USA, the EU and others, without any formal role.”
Although he did contribute to the political process, Mr Blair felt the post was “limited” to supporting the Palestinian people on economic development and strengthening institutions, the source said.
But despite the “political constraints” of the position, Mr Blair believes “much has been achieved” over the last eight years.
The former Labour prime minister feels an “entirely new approach” is required to find a two-state solution, the source added.
Mr Blair will now “concentrate on strengthening relations between Israel and the wider Arab world”, which he believes could help “underpin international efforts to end the ongoing impasse in the peace process”.
‘Hope draining away’
“He will also focus on encouraging Israel to take measures which will dramatically improve the daily lives of Palestinians in Gaza,” the source said
“He believes that achieving this progress on the ground is an essential prerequisite to strengthening broader Arab-Israeli relations.”
James Robbins, BBC diplomatic correspondent, said Mr Blair’s time in the role had coincided with “hope draining away throughout the Middle East peace process”.
He said the Quartet of powers was now likely to examine its own role in the peace process – as well as the future role of another possible envoy.
“So little has been achieved – arguably nothing has been achieved – in the Israel-Palestine process in the past decade and more, so I think if the Quartet examines its own usefulness it will certainly think twice before rushing to have a new envoy,” our correspondent added.