The 26-year-old has signed an 18-month contract after joining from Blue Square South side Team Bath, the club affiliated to the University of Bath.
The England Universities midfielder has graduated from his teaching degree and is to move nearer his Liverpool home.
Abbott, who has been training with Wrexham, could make his debut against Mansfield in the FA Trophy on Saturday.
The former Wigan Athletic trainee has also played in a few reserve-team games and has gained clearance from the Blue Square Premier League and the Football Association of Wales.
Saunders replaced Brian Little in the Racecourse hotseat on 2 October and has inspired Wrexham up the Blue Square Premier table.
Meanwhile, Wrexham have won their appeal to Sam Williamson's sending off against Southport in the Setanta Shield so the on-loan defender from Manchester City escapes a three-match ban.