Wolves would've been Abraham's third team in just a few short months, raising questions over his eligibility. FIFA rules state a player can be registered by three clubs in a single season, but only play for two.
The club had reportedly received permission from the Premier League and Football Association to go ahead with the signing, but The Telegraph's John Percy said FIFA had yet to rule one way or another.
It's a welcome development for Villa, who've relied on Abraham's contributions to stay competitive in the Championship. The striker scored a league-leading 16 goals in the first half of the campaign.
Premier League clubs had enquired about Abraham's availability, but the 21-year-old reportedly told parent club Chelsea that he'd only consider a permanent transfer.
Abraham showed up for training as usual Tuesday at Villa's Bodymoor Heath ground.