Tinkler took charge of the Chilli Boys in August after the club sacked Dan Malesela for the second time barely three games into the season.
The ex-SuperSport United boss then decided to rope in the services of Kobola, who was released by City at the end of 2017/18 when his contract expired.
The duo started their reign together at Chippa with a 2-1 league loss at SuperSport last week.
"Vincent and I spent a year at Cape Town City and by then already I was considering him as an assistant coach because Vincent has been a captain for many years. He’s a leader and a great professional," Tinkler said of 33-year-old Kobola.
"Some of the players respect him highly. When I say that I don't only refer to Cape Town City players but he gets calls from many players, be it from Chiefs or Pirates, asking for advice because he has been in the league for 16 years.
"That experience you can't buy anywhere. He is somebody I know and I trust. He is not here as a yes man because he voices his opinion like he did as my vice-captain at Cape Town City."
Chippa, who are propping up the Absa Premiership table with a point from four games, will next host Baroka on September 15 after the FIFA international recess.
Malesela recently landed a job with National First Division outfit TS Galaxy.