The former Arsenal youngster has penned an 18 month deal at Whaddon Road.
Wynter, 21, spent time on loan with Cheltenham earlier this season, making six appearances and scoring one goal – the winner at Tranmere Rovers.
His final appearance for City was as a substitute against Cheltenham in the Johnstone's Paint Trophy second round tie at Whaddon Road.
"Jordan is an exciting prospect and he fits into what we are trying to do here," boss Paul Buckle said.
"He is good for both short and long term because he is strong enough to play in this division now, as he showed earlier in the season."
"We fought off competition from other clubs in League Two to bring him here."
"He is big and powerful, but also mobile. His upbringing at Arsenal and Bristol City has been fantastic, so I am thrilled he wanted to join us."
Wynter joins loan duo Denny Johnstone and Wes Burns and fellow permanent addition Eliot Richards in joining Paul Buckle's Robins on transfer deadline day.
Meanwhile, striker Terry Gornell has left the club and signed for Accrington Stanley.
One more permanent addition – an out of contract striker – is due to complete his paperwork on Tuesday morning.