A fee will be paid for the 21-year-old centre back, who impressed as the Romans earned a National League South play-off place.
Manager Jerry Gill backs the defender to make an impression in the second tier after City gave him a huge opportunity.
Gill told the club’s website: “Having sat with Robbie in the summer and discussed his football ambitions, it was clear he had the desire to return to professional football.
“During the season his commitment, application and willingness to learn saw him make huge strides in all areas of his game.
“I am delighted he has secured his move to Bristol City, further enhancing our ongoing relationship with Brian Tinnion and the Robins.”
Candy added: “It’s been a great year in so many ways, unfortunately we couldn’t get the promotion we all wanted.
“This summer I’ve been given a great opportunity to play for Bristol City. I therefore wanted to take this time to say thank you to everyone associated with Bath from Jerry, Paul, my teammates, and the fans for the support home and away all season. I wish Bath City all the best in the future.”
Bristol City Chief Executive Mark Ashton said: “Robbie is an exciting young talent and I’m delighted he has signed.
“I am sure he will continue to flourish under the guidance of our dynamic coaching and performance staff.”