He put pen to paper at the Manor Ground, despite an 11th hour bid from Third Division Exeter.
The bid from Exeter, say the club's administrators, was higher, but the 21-year-old forward was reluctant to sign for them.
Abbey said: "Oxford are a better club, playing in a higher league, and is a more convenient place to get to from my London home."
Town have received £30,000 for the marksman.
UNIJET LEAGUE, div 3: Haywards Heath 3 (Steve Agyei 41, Anthony Handley 43, 49), Ansty 2 (Ollie Rowland 65, Terry Hall 75)
Converted for the new archive on 30 June 2000. Some images and formatting may have been lost in the conversion.
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