The 21-year-old had been on the transfer list at his own request since June and has put pen-to-paper on a two-year deal with the Baggies.
"Reuben is a young, exciting, talented player," Di Matteo told the club's official website.
"He has a lot of potential to improve. He scored a lot of goals last season and has a lot of pace. He will give us a different option."
"We have signed Reuben as a squad member and everyone is going to have to be patient as we slowly introduce him."