Mark Harper has become the 12th candidate to join the race for the Conservative leadership.
The backbench MP, who was a minister in David Cameron's government, said he could offer a "fresh approach" to "deliver on the promises we have made".
His rivals to replace Theresa May include five current and four former cabinet ministers.
The winner of the contest, expected to be announced by the end of July, will also become prime minister.
Mr Harper, MP for the Forest of Dean, was a minister in the Home Office and Department for Work and Pensions during the 2010-2015 coalition government and is a former chief whip - whose role is to maintain party discipline and ensure its MPs vote with the government.
Who will replace Theresa May?
The winner of the contest to lead the Conservative Party will become the next prime minister.
He resigned as an immigration minister in 2014 after it emerged that his cleaner did not have permission to work in the UK.
Mr Harper told BBC Radio Gloucestershire that, while he had ministerial experience, it was an advantage that he had not served in Mrs May's government and he considered himself to be "the underdog in this race".
"Most people think that, particularly on Brexit, the current government hasn't got it right," he said.
"The prime minister has taken most of the responsibility for that... but there's a cabinet there and my judgement is, they have been responsible as well.
"I think a new start with a fresh approach is required and I am the only candidate who hasn't been part of her administration, and I think I can bring that new approach which can hopefully deliver on the promises we have made."
Mr Harper, who backed Remain during the 2016 EU Referendum, said: "I'm a democrat and I want to deliver Brexit."
He said he believed there would need to be a "short, focused" extension to the current 31 October Brexit date to allow for a deal to be renegotiated.
But he added: "My preference is to leave with a deal. I think that is what is best for the UK and the constitutional integrity of the UK, but if I am faced with the choice between not leaving at all and leaving without a deal, then I would leave without a deal - keep 'no deal' on the table."
Meanwhile, the business lobby group the CBI has warned that a no-deal Brexit would do "severe" damage to businesses, in an open letter to the Tory leadership candidates.
Former Conservative leader Iain Duncan Smith has said the rules of the contest should be changed so candidates need more MPs to back them before running.
On Thursday, he told the BBC the current threshold for nomination - the support of two MPs - should be "much higher" and the contest should be speeded up.
But Charles Walker, co-chairman of the Conservative 1922 Committee, said: "We're not going to artificially limit the number of candidates who can stand."
The other declared candidates are:
- Brexit minister James Cleverly
- Environment Secretary Michael Gove
- Health Secretary Matt Hancock
- Foreign Secretary Jeremy Hunt
- Home Secretary Sajid Javid
- Former Foreign Secretary Boris Johnson
- Former Leader of the House of Commons Andrea Leadsom
- Housing minister Kit Malthouse
- Former Work and Pensions Secretary Esther McVey
- Former Brexit Secretary Dominic Raab
- International Development Secretary Rory Stewart