The 19-year-old is Sean O'Driscoll's first summer signing as he looks to get the Robins back into the Championship at the first attempt.
Wynter, a tough-tackling central midfielder, has penned a two-year deal after turning down an extended contract with the Gunners.
O'Driscoll told the club's official website: "Jordan is a versatile player schooled at Arsenal Football Club.
"He is comfortable in possession, strong physically and a welcome addition to the club as we try to change the dynamic of the squad.
"He is a young player we feel we can develop, and one that has all the desire and hunger to succeed."
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