Mr Johnson, who led Labour’s Remain campaign, said the former Prime Minister had given the “right message” and it was up to the people to decide on leaving the EU if it does not improve.
Speaking on Daily Politics, the former home secretary also said the views of Mr Blair and Labour leader Jeremy Corbyn on Brexit were “quite similar” – despite Mr Corbyn’s comments that the three-time election winner’s speech was “unhelpful”.
Mr Johnson, who declared he had a “great deal of appreciation” for Mr Blair, said: “It’s certainly the right message.
“The message that Tony was putting forward was that it was absolutely right to trigger Article 50. ‘The will of the people must prevail’ was his opening remark, it’s very much my view as well."
Alan Johnson said Tony Blair's message was the "right" one
Tony might be rather embarrassed by this and so would Jeremy Corbyn, but their views are quite similar
The MP for Kingston upon Hull West and Hessle added there would be a time when the British people would have a choice between leaving the European Union on the terms of the negotiation.
He argued presenter Jo Coburn’s suggestion Mr Blair was forced to give the speech because Labour had failed to oppose Brexit was a “misreading” of his view.
“We’ve been assured in Parliament by David Davis, by Theresa May, by Liam Fox that actually they can negotiate terms that will not be detrimental at all to Britain,” he said.
“Tony might be rather embarrassed by this and so would Jeremy Corbyn, but their views are quite similar."
Remoaner-in-chief: Blair's Views on Brexit Fri, February 17, 2017
Blair will just not give up.
Play slideshow AFP/Getty Images 1 of 6
'It can be stopped, if the British people decide that having seen what it means, the pain-gain analysis doesn’t stack up'
On Mr Blair’s speech, he added: “It was very helpful in terms of setting us out, not least of all because Tony mentioned the fact that it must be up to Europe to reform as well.
“If at the end of this package Europe hasn’t changed at all, it’s still the same rules on free movement then I think people would choose whatever the alternative is to staying in the EU.”
Piers Morgan today joked on Good Morning Britain that Mr Blair had “plunged a 10 foot knife into the back of Corbyn” by calling for another referendum to prevent the Prime Minister from triggering Article 50.
"Tony Blair is out and about, he’s clearly sensing blood with Jeremy Corbyn, possibly even planning another run as leader,” he said.
“He made it absolutely clear that [Brexit] is a disaster, we should reverse the whole thing, the British people have all woken up and there’s been a terrible mistake and they should all be given the right to reverse.”
Mr Blair’s speech on Friday for pro-EU group Open Britain was at the London headquarters of US financial media giant Bloomberg.
The ex Prime Minister described it as his “mission” to persuade the British people they had made the wrong decision in the EU referendum and had “voted without knowledge of the true terms of Brexit”.