The pair haven't played since the win over Newport County in the FA Cup a fortnight ago.
Jesus has been out with a hamstring problem, while Stones has been struggling with a groin strain.
Guardiola says they are now fit and ready for selection but revealed Fernandinho and Aymeric Laporte, both of whom were injured during the Carabao Cup final at Wembley last weekend, are still some way off a return.
“Gabriel is back,” Guardiola confirmed. “John is coming back too, like Gabriel.
“He was injured, and he made his first training session today,” he said. “He’s not in the squad but he can play.”
City currently sit second in the Premier League table, one point adrift of leaders Liverpool with 10 matches left to play, making Saturday's trip to Bournemouth another vital game.
But with City still involved in three competitions, our schedule continues to provide plenty of challenges.
The game against Bournemouth comes on the back of seven matches in 25 days, including a gruelling 120-minute Carabao Cup final against Chelsea.
It means less training and more recovery time for the squad, something Guardiola accepts as part of the demands of a top side.
“Champions League is here, we have the FA Cup. So just focus on the players, let them recover well," he said.
“I was impressed after 120 mins [against Chelsea] how well they play against West Ham. We did incredibly well.
"But now the recovery is less. We don’t play at 8pm like West Ham, we play at 3pm. So we aren’t training, just recovering.
"Bournemouth are completely different at home from the team who play away. They beat Chelsea 4-0 not long ago!
"That’s my concern, not the future, the pressure. It makes no sense, nobody knows.
“We are in a position, 30 points to play for, 10 games left, one point behind Liverpool,” he said. “Lots of things will happen. Anything can happen."