"The reason I am putting myself up for the leadership is because I want New Zealand to be an even better country."
He said he wanted to hold the "shambolic Government" to account.
"I'm not scared of taking on an opponent."
Mitchell said he has "very strong support" but would not state how many MPs were backing him. He ruled out going for the deputy leader role.
Mitchell dismissed talk of National requiring "generational change stuff."
He said he was disappointed when Labour leader Jacinda Ardern had said it was her generation's turn.
"When you're the leader of a country, you lead for all generations."
Mitchell said the main priority was to hold the Government to account. Of NZ First and Labour, he said: "You've got seven per cent that is starting to control 34 per cent. And they are going to have to deliver."
Mitchell said he was on good terms with NZ First leader Winston Peters through the Parliamentary rugby team.
"But Winston is on notice. If I am leader - he's in Government, we're in Opposition. We are going to hold him to account."
He pointed to the difference of opinion over the waka jumping bill as a sign the Government was already starting to fight internally.
Mitchell said he was not concerned the National leadership race would turn nasty. "It will be an open and fair race."
He would not say who he would like as his deputy.
Mitchell also signalled Steven Joyce would be kept on as finance spokesman, saying he was doing an amazing job.
Mitchell said he had discussed running for the leadership with his wife Peggy and the five children they have.
He said he was approached by members of caucus and asked to stand some weeks ago, but admitted he was caught "out of left field" by the timing of English's resignation.
He said he had wanted English to stay as leader. "I personally felt if we call got in behind him he could have taken us through to a win in 2020. But I accept it was a personal decision for him. He's given 27 years to this country."
Mitchell has hired Clark Hennessy - a former staffer - to help with his campaign. Hennessy was one of those NZ First leader Winston Peters had included in legal action over the leak of his super overpayments.
Mitchell was a member of the police armed offenders squad and went on to become a top international hostage negotiator, and established a security consultancy in the Middle East.
He has been in Parliament since 2011 and was Minister of Defence prior to the change of Government last year. He will be the least politically experienced of the four contenders.
Mitchell's announcement today means there are four candidates for leader, with Judith Collins, Simon Bridges and Amy Adams also running.
Steven Joyce is also yet to show his hand after revealing he was considering it himself.
The replacement for outgoing leader Bill English is expected to be voted on by the National Party caucus in eight days.