Grant spent the 2006/7 season as Pompey’s technical director before joining Chelsea as director of football.
The move to bring back Grant comes just 48 hours after Ali Al-Faraj took over the club from Sulaiman Al-Fahim.
Grant has signed a three-year contract with Pompey.
“I am happy to return to the best league in the world, the English league,” he told Israeli website One.
Pompey chief executive officer Peter Storrie said: “The club’s new owners want to appoint with immediate effect, Avram Grant as director of football.
“Paul Hart remains as manager and Avram Grant will work alongside him and give him the benefit of his experience. Avram’s role is to help and advise Paul. Team selection matters will remain with the manager.
“We now have two very experienced people working together which will only benefit the club. Paul does not have an assistant but now has a director of football alongside him.
“The manager, director of football, chief executive officer and chief scout will all work together on the buying and selling of players.”
