The 23-year-old has signed a two-year deal with the Gas after a goal-den season in the National League South.
His form in the box for the Hawks took Paul Doswell’s team to second - and earned him a share of the Golden Boot award.
He scored 24 times in 41 games across two spells at the club and boss Doswell believes he can make the step up.
Rovers manager Ben Garner says Ayunga has been a long-term target - and thinks he can keep the net bulging three leagues up.
"Given the season he has just had there was interest from a number of EFL clubs and we are very pleased that we have managed to agree a deal that will see Jonah play here," Garner said.
"Jonah has had an outstanding season in front of goal and I’ve been really impressed by both his desire to join us and his hunger to improve.
"He's coming off the back of featuring in the National League play-offs for Havant and Waterlooville, so he's in good shape to join up immediately with the rest of the squad.”