"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," chief executive Peter Storrie said on the club's website.
Grant will take charge of the league's bottom team for the home game against Manchester United on Saturday in his role as director of football. The club will then apply to switch his work permit status to manager.
"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," Storrie added.
PORTSMOUTH REUNION
The 54-year-old former Portsmouth technical director returned in October shortly after Saudi Arabian businessman Ali al Faraj's takeover of the south-coast club.
Grant was at Portsmouth for 13 months from June 2006 before replacing Jose Mourinho at Chelsea and, despite becoming the only manager to take the west London club to the Champions League final, he was sacked in May 2008.
The Israeli faces a very different challenge at Portsmouth trying to keep the club in the Premier League.
Portsmouth have endured a miserable season, having became the first English top-flight side in 79 years to lose their opening seven games of the campaign.
They are four points below the safety zone after 13 games with their position unlikely to improve with matches against United, Aston Villa, Chelsea, Liverpool and Arsenal this year.
Former manager Hart steered Portsmouth away from the drop zone last season but was hindered this term by financial restrictions at the troubled club.
Al Faraj bought 90 percent of the shares last month from Sulaiman al Fahim, who had taken over in August but struggled to refinance Portsmouth's debts.
Al Fahim, now a minority owner, earlier this month told Reuters a transfer freeze imposed by the Premier League in October for unpaid debts to other clubs would soon be lifted.
"We will have our first official board meeting on December 1 and I am giving back the property rights to the club so they can upgrade the current stadium," Fahim said on November 15.
In September, payments to some of the first team squad were delayed, highlighting the club's problems.
