The 18-year-old, who can play on either wing, has been added to training sessions with the first team squad recently having been a regular scorer for the Robins' under-18s.
"We're delighted for young Wes to have accepted our offer and he's very happy about it," manager Derek McInnes told the club's official website.
"He's developed ever so well over the last few months, and we see real potential for improvement in him going forward. Now the deal is done he can just concentrate on his football.
"He's quick, he's getting stronger all the time and he's decent in the air. He's had good experience in the Under-18s and more recently the Under-21s."
Earlier this month 15-year-old Wales youth international Joe Morrell signed scholarship terms with the club, with the aim of turning professional with the Ashton Gate club, despite interest from Premier League sides.