Alexandre Gaydamak and Peter Storrie made the decision in a meeting prior to Pompey's 1-0 defeat to Chelsea at Fratton Park.
A resurgence in form has been attributed to the move initiated by the Blues owner and the club's executive chairman, with Hart and Kidd claiming four points from their three games in charge.
The pair took the reins of the struggling south coast club in time to lead the team to a 2-0 home victory over Manchester City - their first Premier League win since November 30.
Storrie said: "Sacha (Gaydamak) and I have been delighted with how the team have fared under Paul and Brian's control.
