The New Zealand government has said it would have preferred the tour to be cancelled but would not prevent it going ahead.
"I know that not to go would cost New Zealand cricket money. I've said myself I wouldn't be seen dead there. I'm very concerned about what's happening in Zimbabwe," Prime Minister Helen Clark said on Television New Zealand.
Mugabe's government has been pulling down thousands of homes and businesses, leaving hundreds of thousands homeless in winter, according to the United Nations. The destruction targeting mostly poor areas has been condemned worlwide and follows March elections described as a sham by foreign governments.
New Zealand Cricket (NZC) chief executive Martin Snedden said NZC would have to pay a fine of at least $2 million if it called off the five-week tour including two Tests and a One-day series with the hosts and India.
Players were given the choice of withdrawing from the tour as individuals but had decided unanimously to go ahead after the trip was cleared by a Zimbabwe-based independent security expert, Snedden said.
No pressure had been put on the players, who were told they could boycott the tour with no financial penalty.
They were given information about Zimbabwe's political situation and had the past two months to decide, he said.
"My understanding is the players are reasonably confident in the way we handle it and are prepared to trust us to do it right."
Snedden said the New Zealand government had suggested the touring side tried to avoid any contact with Zimbabwean government officials and it would try to follow that advice.
The tour will mark the return of fast bowler Shane Bond who has been out with a stress fracture since May 2003.
Bond, 30, has 43 wickets from 10 Tests at an average of 24.30, and 51 wickets from 27 One-day Internationals at 19, with a best of six for 23 against Australia at the 2003 World Cup.
All-rounder Jacob Oram also returns from a stress fracture which has kept him out of international cricket since January and off-spinner Jeetan Patel has been named for the first time in the One-day squad.
The Zimbabwe itinerary has not yet been released, but the first Test is expected to start in the second week of August.