George Osborne says he will stay in the Commons to "fight for the things I care about" as he launches a think tank to promote his Northern Powerhouse plan.
Mr Osborne, who was sacked as chancellor by Theresa May, said: "I don't want to write my memoirs because I don't know how the story ends."
There had been a "bit of a wobble" by Mrs May over the project, he said.
No 10 says Mrs May is building on his plan to create a northern economy to rival London and the South East..
In his first major interview since being sacked, Mr Osborne told BBC Radio 4's Today programme: "Politics is a tough business." But he said he believed he could "push and fight for" ideas he backed from outside the cabinet.
The MP for Tatton in Cheshire returned to the back benches following Mrs May's cabinet reshuffle, and said chairing the new body - the Northern Powerhouse Partnership - would "now be a major focus of my political energies".
Analysis by Ben Wright, BBC political correspondent
A mere two months ago George Osborne was the second most powerful member of the government. Then he was the first cabinet minister Theresa May sacked when she became prime minister, dispatching him to the backbenches.
Politics is brutal. But if Mrs May hoped the former chancellor would disappear she was wrong. While David Cameron has opted for memoir writing and - it's safe to predict - a future on company and charity boards his old ally is staying in politics.
The board of the not-for-profit organisation will include business figures from across the north of England, as well as political figures. Its aim is to devolve powers and funds to northern city regions, improve transport links and create new regional mayors to act as figureheads.
Asked why he felt he had to say "the Northern Powerhouse is here to stay", Mr Osborne told the BBC: "To be honest, there was a little bit of a wobble about when we had the new administration about whether they were still committed to the concept of the Northern Powerhouse."
He said he supported economic development across the whole of the country and he had "sweated blood" to get a mayor for Birmingham - but he felt there was a particular opportunity in the North of England because the cities were close together.
Pressed on whether he intended, like his former Downing Street neighbour David Cameron, to quit politics, he said: "No, I'm not."
He said he wanted to "hang around and find out" how his story would end, adding: "There's an enormous opportunity now to take part in the decisions that are going to affect Britain... And I want to be there in ultimately, still the place where these decisions are made, the House of Commons, and be part of that decision-making process. Because I want to fight for the things that I care about."
He said he had voted for Mrs May and she was "the best person for the job of the candidates who put themselves forward" and she had made a "strong start".
She was "perfectly entitled to set the tone" of her administration, including "to take a pause and consider" big decisions like whether to go ahead with the £18bn Hinkley Point nuclear power station.
But he added: "I don't think anything has fundamentally changed from the deal that we put together in government just a few months ago... it looks to me pretty much like the same deal."
On Mrs May's controversial plans to expand grammar schools, Mr Osborne said the new prime minister was "perfectly entitled to set out new ideas" and he supported her goals. But he said grammar schools focused "80% of the political discussion" on where 20% of the children go.
"I'm not against new grammar schools opening up where areas want them, but I think the real focus of education reform remains the academy programme, transforming the comprehensive schools that most people in this country send their children to."
'One of the grown-ups'
Asked about former energy secretary Ed Davey's comments that Mr Osborne and Mrs May had "really disliked each other" when in cabinet together, Mr Osborne responded: "That's genuinely not true. I've worked with Theresa for 20 years in opposition and in government. I actually think she's a person of integrity and real intelligence, and frankly in a Cabinet that included people like Ed Davey, she was one of the grown-ups."
Mr Osborne backed the Hinkley deal and championed the Northern Powerhouse project as chancellor, before being sacked from the cabinet by Mrs May when she became prime minister.
Earlier this month, Labour's mayoral candidates for Greater Manchester and the Liverpool city region urged Mrs May to "honour your promises to the north of England", amid reports that she intends to shift the focus to other areas.
However, Downing Street has denied any lack of commitment, saying Mrs May is building on Mr Osborne's project, having put Treasury aide Neil O'Brien in charge of it in her policy unit and appointing a Northern Powerhouse minister, Andrew Percy.
Crossbench peer Lord Kerslake, who chairs the Northern Powerhouse's advisory board, said it "remains unclear" which direction Theresa May would take the Northern Powerhouse and Mr Osborne wanted to "hold the new government's feet to the fire".
At a news conference, Mr Osborne said he had not spoken directly to Mrs May about the project but had spoken to Communities Secretary Sajid Javid who had been "very supportive".
Mr Javid said the government "realises the huge untapped potential of our great northern towns and cities" and he hoped the new partnership would "become an important part of the debate".