The Prime Minister told The Yorkshire Post that "in principle" a region-wide devolution agreement backed by the majority of its political leaders was the right thing to do to end the deadlock over vital powers and resources being handed over from Whitehall.
He said it was for local people to decide what the best boundaries were but that based on his experience as mayor in London, where the mayoral authority covers a large urban and suburban area, "you want to have a pretty diverse area and a big area".
Ministers in his predecessor Theresa May's government refused to back the detailed proposal on how a devolution deal covering all of Yorkshire could add £30bn a year to the region's economy, saying it was too big and diverse for a single mayor to cover.
But Mr Johnson said: "In principle I am mad keen on it. My experience is that the way to drive things like infrastructure spend and the way to champion a local area is that you have got to have political figures who believe in it, who love it and will stand up and mount the barricades and say 'come here, invest now'.
The Prime Minister warned he did not want to repeat what he described as "the tragedies of the 1970s and 1980s when you had very irresponsible left-wing local governments who totally ruined the reputation of local government".
He added: "The key thing is that with power comes responsibility. If we do it then he or she has got to take the burden on for raising the taxes as well.
"Look at Andy Burnham in Manchester, I think he is being very active but I would like to see some responsibility.
"When I was mayor of London I had to do the fare box, the police precept, I took the hit if passengers thought I was charging them too much for their tube journeys and they often did, they would demand improvements.
"You have got to have that political responsibility. What you can't have is a mayor for Yorkshire who has just is always holding out the begging bowl to the Treasury."
It came as the Prime Minister faced a growing backlash over the use of West Yorkshire Police trainee officers as the backdrop for a speech in Wakefield which he used to attack Labour's position on Brexit.
Amid criticism from Labour politicians, the Chief Constable of West Yorkshire said he was "disappointed" at the way the officers were used and that he had not been told about the subject of the speech.
Yorkshire is yet to achieve a full devolution agreement, leaving it lagging behind areas like Manchester and the Tees Valley where metro mayors have a range of powers previously held by central government.
A coalition of local authority leaders has handed detailed proposals about a Yorkshire wide mayoral authority to the Government, but so far met with resistance.
Talks are currently ongoing between Yorkshire leaders and Whitehall officials over possible 'interim deals' covering smaller city regions.
Backers of a One Yorkshire deal welcomed the Prime Minister's words. Judith Blake, Leader of Leeds City Council said: “We’re delighted that the Prime Minister has given the green light to progressing One Yorkshire and we look forward to meeting his officials at the first opportunity to take things forward.
"Yorkshire is prepared and ready to take on more responsibilities and deliver the improvements that would allow our great county to reach its full potential.
“Officials under previous Prime Ministers asked us to come up with the solution that would work best for Yorkshire and the result of those deliberations was the One Yorkshire proposal.
"Up until this point One Yorkshire hasn’t received the Government support needed for it to progress, so the words from the Prime Minister are very encouraging but the main thing is that he now delivers on what he has said.”
Sheffield City Region mayor Dan Jarvis said: "In spite of the current political turmoil surrounding Brexit, we mustn’t lose sight of the need for more effectively targeted investment in the North. Devolution is a critical component of this.
"There is widespread support for a Yorkshire wide devolved arrangement that would deliver significant economic benefits. Leaders from across Yorkshire stand ready to work with the Government to make it happen.”
John Grogan, Labour MP for Keighley and co-chair of the One Yorkshire Committee, said: "This could be a breakthrough moment for the campaign for one Yorkshire devolution.
"The Prime Minister speaks as someone who has held the office of Mayor of London and knows the importance of having a champion for an area who can drive change forward.
"If a General Election is delayed for a few weeks the Prime Minister could do worse than using the time available to set the Government firmly on course to legislating for the election of a Mayor in Yorkshire in 2022.
"Our goal is to get all the major parties backing this idea in their forthcoming election manifestos."
Analysis - Rob Parsons
Even by the standards of his short but eventful premiership so far, it had been a bruising day for Boris Johnson as he arrived at The Yorkshire Post’s offices in Leeds.
With a coterie of advisers and his security detail in tow, he made the trip on a day where he found out his brother was quitting politics and he faced hostile questions from the Press over his troubled Brexit strategy.
A trip to Morley in West Yorkshire, part of a marginal Tory-held constituency he would hope to defend in any upcoming election, saw him faced with hostile locals and one who told him to “leave my town”.
The launch of a recruitment campaign for new police officers brought criticism for politicising a group of trainees who stood behind him as he lambasted Jeremy Corbyn.
One of the group, who had been kept on her feet due to the delayed speech, became unwell. Mr Johnson later told The Yorkshire Post he felt “very, very bad” about what happened but that the officer was “right as rain”.
“I saw her afterwards, Helen, she is called. She was fine. She was wonderful. It was just being on her feet for so long.”
Given the torrid day he’d had, the PM was surprisingly perky during his interview at The Yorkshire Post’s office in central Leeds. And his warm words on devolution and infrastructure were unmistakenly those of a man who hopes to be winning over local voters in the not too distant future.
As recent polling for this newspaper shows, people in Yorkshire are distrustful of politicians’ promises and many don’t believe Mr Johnson when he pledges to improve northern transport.
But perhaps a more pressing concern for the PM – as he struggles to find a way to avoid having to make the highly unpopular move of delaying the Brexit process – is that he may not be in the job long enough to try and deliver on them.