Baggies boss Roberto Di Matteo has confirmed that the 21-year-old winger is set for a three-month loan move to London Road.
"Peterborough have been chasing Reuben for a while now," Di Matteo told his club's official website.
"I recommended to Reuben to go and play because he will hopefully play week in, week out.
"It's always better to play than be on the bench and play ten minutes here and there or a reserve game.
"It's very important for him to get football at this level and we'll see how he gets on."