Bridges said Bennett was a "massive talent" with huge strengths who would make an excellent deputy.
"I'm really glad I've done this."
He said there had been strong candidates and he was excited about the opportunities.
"I know that Bill English and Paula Bennett are going to do a fantastic job."
He said he and Bennett were "great mates" and he had talked to her about his decision to withdraw this morning.
"I rang her up, I think my first words were 'Deputy Prime Minister' and I wished her all the best," he said.
"Paula is someone I have a huge regard for."
He said it would be a new Government and he was looking forward to a role in the new team.
Bridges spoke to Bill English this morning and discussed his withdrawal.
He was pleased to have been in the race and that there was a real contest.
Bridges said Bennett's strength was her ability to connect with people, and her strong policy background.
"It was hard to go past her as a top candidate for the job."
"I think they're going to be an exceptional combination," he said.
"I know they are the strongest team we have for the National Party, for our unity, for the Government ... and for the election."
Bridges was not expecting any backlash from the back benches.
Bennett had public declarations of support from 23 MPs last night to Bridges' 10 - and was understood to have enough private support to get her over the 30 votes needed in National's caucus of 59.
The caucus was due to vote on it on Monday, but unless there is a last minute entry at that caucus meeting it appears set to be a pro forma appointment.
MPs backing Bennett pointed to reasons including her Auckland base, compared to English's Wellington and South Island roots, as well as the male/female balance and her gregarious personality as a contrast to English's restraint.
English had not expressed a preference, but has worked closely with Bennett in Government - both in developing the 'investment approach' in her former social development portfolio and on housing.
Bridges said he worked well with English and had a fantastic relationship with Bennett.
"I want to be a strong part, a key player in his team and I feel like I can be."
He would not be drawn on what ministerial portfolio he would seek under the new leadership team.
Bridges said he was not pressured to leave the race.
"This is entirely my decision."
