Writing in The Sunday Mirror, Lord Prescott said he would have laughed 20 years ago if anyone had suggested Jeremy Corbyn could ever lead the party.
But, in his strongest expression of support yet for the Labour leader, he said Mr Corbyn was now transforming into "a prime minister in waiting".
Lord Prescott, who served as Tony Blair's deputy leader from 1994 to 2007, said he would be out on a battle bus campaign for Labour in home-town Hull on Sunday and across the North over the two and a half weeks before the June 8 General Election.
He hailed the programme unveiled by Mr Corbyn on Tuesday as "the best manifesto Labour has published since 1997".
Lord Prescott, who represented Hull East from 1970 to 2010, added: "Protecting pensioners, scrapping tuition fees, taking water and energy into public ownership.
"Yes, it's left. But it's also right. Polls have shown that the policies are popular."
Lord Prescott acknowledged Mr Corbyn faced a challenge winning over the public, which he blamed on "biased" media attacks and the no confidence vote by 173 of his own MPs.
But he said: "The polls are changing.
"The more people see him on TV, speaking to huge crowds and on the doorstep, the more they're seeing the real Corbyn...
"You will have a very clear choice this election - a Poundland Thatcher peddling the same old Tory lies and broken promises.
"Or a Labour campaigner who finally looks like a leader.
"Things did get better under Labour.
"They can get better again if we make June the end of May."