Anchorage had been in talks with Burger King's local owners, Dennis Jones and Mark Backhaus, for some months, The New Zealand Herald reported.
It officially took over ownership of the 69 company-owned and two-franchised Burger King outlets yesterday.
Anchorage partner Mark Bayliss becomes chairman of the New Zealand Burger King operation.
He would not reveal what the firm had paid except to say it typically invested in businesses worth $50 million to $150 million.
"It's very much in that sweet spot."
Mr Bayliss said Anchorage liked established brands that were underperforming.
Burger King was nicely established but had reached a stage in its evolution where it needed new capital.
Anchorage planned to invest in the brand and the existing network, and to expand the number of outlets. It was not planning redundancies.
