The 21-year-old has agreed to move to the League Two club following a successful trial.
The Grecians are yet to confirm the length of Wheeler's contract.
"He's strong and quick, but he's also bright," City boss Paul Tisdale told the club's official website.
"He'll work for the team - he's infectious and hard-working and has something about him."
Wheeler could feature in Exeter's opening match of the season against Bristol Rovers on Saturday.