The 25-year-old striker has scored 20 goals in National League South games for the Wings this season.
He has netted a further seven times in three FA Cup games, including six goals in one game against Swindon Supermarine in the third qualifying round.
Ex-Notts County and Bromley man Coombes is eligible to make his debut for the U's against Torquay on Saturday.
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National League side Sutton United have signed former Chelsea trainee Adam Coombes from Welling United.