The Coventry born defender, who played for City in the early 1980's, was caretaker boss last season and has been given the job again after John Ward left the club by mutual consent. Abbott was manager when City played at Carlisle in the League Cup.
The Cumbrians were unbeaten in their first five matches but have lost their last ten and have slumped to 20th in the League One table.
A club statement read: Assistant manager Greg Abbott has immediately been appointed caretaker manager with the full backing of everyone at the club.
"Greg had been hugely disappointed not to get the manager's job here on a full-time basis last season after having been caretaker manager following Neil McDonald's departure until John Ward's appointment. That was despite having won five and drawn two of his ten games in charge. "We would ask all Carlisle United fans to give their full backing to Greg and the squad, starting with Saturday's FA Cup first-round tie at home to Grays Athletic."