The Financial Times said it had learnt that Blair will be confirmed as the Quartet's envoy by a specially convened meeting of representatives of the four parties, the US, EU, UN and Russia in Jerusalem on Tuesday.
"Blair's appointment has been 150 per cent approved," a source close to negotiations over the new role was quoted say.
"The Jerusalem meeting is all about arranging logistics, making final arrangements and getting the announcement out," the source said.
The expected confirmation comes after reports last week that the Bush Administration has been holding talks with the outgoing prime minister on the role before he formally steps down from office on Wednesday.
But according to the Financial Times, Chancellor of the Exchequer Gordon Brown, who succeeds Blair this week, is "deeply unhappy with the appointment."
It suggested that Blair's role, which is expected to largely focus on only improving Palestinian governance, was certain to distract attention from Brown's plan to seek reconciliation between Israel and the Palestinians through economic means.
There was said to be "unhappiness" at the British Foreign Office, which was not consulted on the appointment.
Last week, shadow foreign secretary William Hague also said he was opposed to the idea as the prime minister was a controversial figure in the region.
In addition, the EU's High Representative Javier Solana was also reported to be against the move on the grounds that it will distract from his own efforts in the region.