He told Newstalk ZB's Mike Hosking his decision was based on change.
"Someone said 'hey, consider this opportunity', and I looked at it, and the friends that knew me talked about where I was in my life, and I thought 'it's an opportunity, let's go for it'."
Brooke said money is not necessarily the driver behind the change.
"It is relevant. I mean obviously it will help in my retirement and I've got to think about that. Teaching is not well paid in any part of a secondary school."
Jack Boyle, from secondary teacher union PPTA, points out that the public school system is failing to retain the leaders it trains.
"They've done a lot of that learning and development in the state system," he said.
"There's therefore been quite a bit of an investment in terms of resourcing and support.
"You'd need to look at what some of those challenges are that might be causing principals to leave public schools and go into private schools so that we can hang on to them."