Robson's closest competitor, Mark Wassung, received 4139 votes. Tony Christiansen was coming in third with 2810.
The confirmed winner will be sworn in at an extraordinary council meeting on Monday.
Twenty candidates put their hands up to fill the at-large seat left vacant by Gail McIntosh's death in January.
Mayor Greg Brownless said he congratulated Robson and offered his sympathies to the 19 unsuccessful candidates.
He said Robson had run on a strong financial management platform.
"[His win] indicates to me that people took a strong stand on the financials."
Brownless, who has not served with Robson on he council before, described him as "fairly forthright".
"He speaks his mind and is obviously very intelligent."
Robson said he heard the news in a phone call from Tauranga City Council chief executive Garry Poole.
"Since then it has been a series of texts and phone calls coming in. I took a break for about 45 minutes and took my partner to lunch at Palmers.
"Of course, there are implications at home. I will be going from being a retired gentleman to back to work. It's a fulltime job."
Robson said he believed the public support he received from sitting councillors Steve Morris and Rick Curach was crucial to his win.
Robson ran a campaign critical of council rates increases and spending priorities, including a proposed Tauranga museum.
His slogan was "real change - guaranteed" and his eye-catching election signage featured a confused baby with thought bubbles.
"Councillors must prioritise infrastructure. Proposing an extravagant museum, when our roads are grinding to a halt, and recycling is going backwards, fails that test," Robson wrote in his election booklet statement.
Robson is a retired management consultant. He ran unsuccessfully for the position of Tauranga mayor in 2007, 2010, 2013 and 2016. He was an at-large city councillor from 2013 to 2016.
Polls for the byelection opened on April 1 and closed at 12pm today. Today's progress result will be followed by a preliminary result tomorrow and a confirmed result on Thursday.
As of 9.30am, just under 29 per cent of registered voters - 27,600 people out of 95,500 - had voted.
Mayor Brownless said he found the voter turnout a little disappointing.
"It would have been nice if we could have got more people voting.
"I think we don't value our right to vote enough."
The results of the museum referendum held alongside the by-election are expected to arrive a little later today.
Byelection progress results
John Robson - 4944
Mark Wassung - 4139
Tony Christiansen - 2810
Bill Faulkner - 1713
Sheldon Nesdale - 1688
Lester Gray - 1607
Murray Guy -1391
Talia Harvey - 1347
Douglas Owens - 1248
Peter Stanley - 1213
Anne Pankhurst - 871
Rosie Dawson-Hewes - 769
Buddy Mikaere - 729
Gillian Cook - 611
MJA Anderson - 345
Andrew Ragg - 249
Yvette Lamare 216
David Tank - 214
Robert Curtis - 88
Zeepra Lemoto - 86.
Source: Tauranga City Council
