The former Chelsea boss will replace the sacked Paul Hart.
Grant will be in the dugout for Pompey for their clash with Manchester United on Saturday.
Pompey chief executive Peter Storrie told the club’s official website: “Avram is a very experienced and respected manager who has managed at the highest level.
“The board believes he is the man to help steer the club out of the relegation zone.
“He knows the club, the players and the set-up at Fratton Park, so it was the logical move to make him the next manager, once the board had decided to relieve Paul Hart of the role.
“He will take charge of training on Friday alongside first-team coaches Paul Groves and Ian Woan.”
