There had been doubts about whether the game would be played after poor weather in Manchester but officials inspected the pitch at 1.15pm and deemed it playable.
Manchester United go into the game seven points clear at the top of the Premier League but face a tough test against West Brom who have impressed this season and currently sit sixth.
Elsewhere the weather has caused several postponements with five matches so far called off in the Football League at Colchester, Stevenage, Cheltenham, Aldershot and Gillingham.