The decision came a day after Monarchy New Zealand released a list of icons that would be illuminated around the country.
Mr Crosby said he was not aware of Monarchy NZ's initial approach to the council about lighting up a monument as a staff member had fielded the call and had not passed it on.
"I have the greatest respect for the Queen in particular, and the royal family. I have had the honour of meeting Prince William in Christchurch. He's an absolutely lovely young man."
Piccadilly Circus manager and British ex-pat Jamie Parkes was totally behind the plan.
"That's really cool. I think that's quite nice. I'm completely imperialistic. I like it. I've always liked how New Zealand portrays and supports them."
Mr Parkes said New Zealanders were far less critical of the royal family than the British media.
Tauranga MP Simon Bridges said it was a great idea and he believed most Tauranga residents would be delighted with it.
"I reckon the Western Bay would probably be more monarchist than most parts of the country. Even those who aren't staunch monarchists love the arrival of a bonny baby."
Mr Bridges said his office was running a sweepstake on the date of birth, gender, weight and name and would be having a party to celebrate its arrival. His bet was on a boy named Simon.
Monarchy NZ chairman Sean Palmer was thrilled to hear Tauranga would be among the cities celebrating the birth.
"This is a well-known theatre and it's got the royal connection," Mr Palmer said.
The original list of 24 monuments had climbed to close to 30 since Tuesday. These include Princes Gates in Rotorua, The Cloud in Auckland, the Wairarapa Times-Age Building in Masterton and Victoria Bridge in Hamilton.
Street View
The city council has decided to light up Baycourt Theatre either pink or blue to mark the arrival of the royal baby. What do you think?
"The people I've talked to don't really care about what sex it is but I think it would be cool. Bayfair might be a good place." - Allie Douglas, 20,Tauranga
"I don't really care about it. The harbour bridge would be good." - Liana Ashford-Jones, 18, Katikati
"I reckon it's a good idea. It should be something more visible, I live in Papamoa. The harbour bridge would be cool." - Kayla McGuinn, 17, Papamoa
"I don't really care one way or the other. I really don't know." - Jen Pratt, 31,Papamoa
"Good idea. I was wondering if we were doing something. They should light up something on the waterfront." - Gordon Golem, 57,Judea
Most popular picks for the royal baby's name
Girl: Alexandra, Elizabeth, Charlotte, Victoria, Diana
Boy: George, James, Louis, Philip, Arthur
Source www.oddschecker.com