These developments, along with other confidential potential developments that are in discussions with the council, will put pressure on the city centre's 3400 car parks.
If approved, the new building will be built on land occupied by an off-street car park on Harington St by the end of 2018.
Councillor Gail McIntosh said it was time to accept the inevitable.
"We have a popular place where people are willing to pay for parking but want to be sure it's available. With this report I think it's where we have to go. Bite the bullet."
Cr John Robson said the debt for the building would be user funded and not ratepayer funded.
"A clever council working with clever staff will make this building more affordable than people think. It's sensible spending by a sensible group of councillors."
Tauranga is a "car-centric city", Cr Rick Curach said, and it was unlikely there would be any major shift to buses or bikes any time soon.