The Quartet - which includes the U.S., the European Union, Russia and the United Nations - appointed Blair to the post in 2007 with the goal of helping develop the Palestinian economy and institutions. The mission was meant to prepare the groundwork for the establishment of a Palestinian state alongside Israel as part of a peace agreement.
But Blair quickly found himself fighting small battles with Israel over the movement of Palestinian goods and people. With peace efforts stalled, the goal of a two-state solution remains as elusive as ever.
One official said Blair had suffered "frustration" with the limited authority of his mandate. The official also said that Blair felt his office has a strong leadership team and that now is the right time to move on.
Read MoreWhyI'm optimistic on the Middle East: Tony Blair
According to his office's website, Blair's office succeeded in helping remove dozens of Israeli checkpoints in the West Bank, easing the movement of workers and Palestinian products to markets. He also helped boost tourism in the West Bank town of Bethlehem, helped secure thousands of permits for Palestinian laborers to work in Israel and helped engineer a $350 million mobile phone investment in the West Bank, creating thousands of jobs.
The official said that Blair remains committed to the Quartet's vision of a two-state solution and hopes to play an "informal" role in promoting peace. One area where he could help is developing relations between Israel and the wider Arab world, the official said.
Read MoreTony Blair: Islam must resolve its internal 'issue'
Follow us on Twitter: @CNBCWorld