The 54-year-old will take charge for Saturday's Barclays Premier League clash against Manchester United at Fratton Park.
Chief executive officer Peter Storrie said: "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.''
The Israeli was due to receive his work permit for his director of football role this week and the club have revealed he will at first continue to work in this capacity.
The club will then "go through the process of making the technical change that will allow Avram to become manager''.
He takes over with Pompey bottom of the Premier League having collected just seven points from 13 games.