Simpson was with the Robins from the age of six, but did not make a first-team appearance.
The 18-year-old is Forest Green's 10th signing since winning promotion from the National League.
"He's box to box, he's good on the ball, so he should be a good addition to the squad," Rovers boss Mark Cooper told the club website.
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Forest Green Rovers have signed former Swindon Town midfielder Jordan Simpson on a two-year contract.