Before the general election, the former Prime Minister refused to personally endorse Mr Corbyn, saying instead people should vote Labour to ensure a proper opposition to Theresa May.
Just a year ago, he said he believed it was impossible for Mr Corbyn to win an election on a left-wing platform, but the recent shift in the political landscape – including the election of Donald Trump as well as Labour’s better than expected result in June – have caused him to change his mind.
But he has not changed his belief that a Corbyn-led Government would be damaging for the country with what he termed “an unreconstructed far-left programme.”
Speaking to Newsnight editor Ian Katz, Mr Blair said: “I accept now what if you’d asked me a year ago I’d have said is impossible - I accept is possible - you have to say in today’s world now, there’s been so many political upsets it’s possible Jeremy Corbyn could become Prime Minister and Labour could win on that programme.
“I still think the surest route is through the centre.
“For most of my political life I’ve been saying ‘I think this is the right way to go, and what’s more it’s the only way to win an election’. I have to qualify that now. I have to say, ‘no, I think it’s possible you end up with Jeremy Corbyn as Prime Minister’.
He added: “You have to say in today’s world now, there’s been so many political upsets it’s possible Jeremy Corbyn could become Prime Minister and Labour could win on that programme - so in that sense I am changing my position, but I’m not changing my mind on the wisdom - at same time of delivering Brexit - of delivering frankly an unreconstructed far Left programme.”
Although he won three elections and was once regarded as one of the shrewdest political operators in recent history, Mr Blair admitted he did not see the Brexit result coming, nor did he anticipate the Trump victory.
Mr Blair said that while he hasn’t changed his core beliefs in the European project and in centrism, he has had to “(accept) that there’s something going on in politics that (I) didn’t get and don’t fully understand.”
Mr Blair has made several appearances this week to call for Brexit to be halted because of the harm he believes it will do to the country.
He said that in the event of a snap general election, the combination of Brexit with Mr Corbyn’s manifesto would be a “difficult” one.
“You can’t rule anything out in today’s politics, but it doesn’t stop me believing that if we deliver Brexit, and at the same time are delivering the programme he has at the moment, unreconstructed, unchanged, we will be in for a very very difficult time as a country.
He repeated his belief that Brexit is “a disastrous mistake for the country”.
“I think it’s relegating us, diminishing us, it’s going to do us damage economically, it’s going to do us damage politically.”
The interview can be watched in full on Newsnight at 22.30 on Monday 17 July.