Mr Crosby was elected for his fourth term as mayor in the October 2013 elections, narrowly beating newcomer and current deputy mayor Kelvin Clout by just 502 votes.
Mr Clout issued a statement soon after Mr Crosby's announcement, declaring his intention to stand for the mayoralty in 2016.
Mr Clout said he had learned a lot and was relishing the associated challenges and opportunities.
He acknowledged Mr Crosby's work despite some difficult circumstances.
"We do not always agree on how best to address the city's issues but I have great admiration for Stuart and the resilience he has shown over many years. He has successfully dealt with major flooding events, the global financial crisis, the Rena disaster and often a dysfunctional council."
Tauranga City councillors spoken to by the Bay of Plenty Times were generally supportive of Mr Crosby's decision and were not surprised by the announcement.
Councillor Clayton Mitchell told the Bay of Plenty Times he would not rule out a go at the top job but was not contemplating it at this early stage. "I am just focused on the next two and a half years ..."
Councillor Catherine Stewart said the announcement was "not a total surprise, given the results of the last election", while councillor Matt Cowley said Mr Crosby's priority was succession planning and passing on his knowledge to councillors.
Councillor Bev Edlin said Mr Crosby had been saying since the last election that he would not run again.
Councillor Steve Morris shared a private message with the Bay of Plenty Times sent by him to Mr Crosby.
"As a 13-year-old I recall watching you in the chamber and wondered at that time if I could one day become a Papamoa councillor too. We were all proud when you won the mayoralty in 2004 and to serve on council with you brings things full circle for me."
While Councillor Rick Curach's thoughts were not quite so positive.
"No surprises - he's taken heed of the message sent at the last election."
Councillor Bill Grainger had a similar opinion.
"I think Stuart has got to the stage where he realises that almost 30 years in local politics is a bit extreme.
"I'd say he is opting to go out with dignity ..."
Gail McIntosh had no comment, while Cr John Robson could not be contacted for comment. Former mayoral candidates Mike Baker and Hori Leaming were also unavailable.
- Additional reporting Natalie Dixon