The former Chelsea manager had a spell with the club alongside Harry Redknapp before moving on to Stamford Bridge in 2007.
The south coast club announced that the 54-year-old Israeli would return to Fratton Park and start work on Monday.
Portsmouth, which was taken over by Saudi Arabian property magnate Ali Al-Faraj on Monday, is last in the Premier League after losing its first seven Premier League games. The team beat Wolves 1-0 on Saturday.
England goalkeeper David James welcomed the appointment of Grant.
"I love Avram, he's a great guy," the Portsmouth 'keeper said at an England news conference ahead of Saturday's World Cup qualifying game in Ukraine. "When I first joined the club he was there and he was very active in preparation for matches. He's a very wise man. His football knowledge is immense. It's a very good move."
James said the arrival of Al-Faraj as the new owner would bring financial stability to the cash-strapped club, which was unable to pay the players' wages on time last week.
"The non-pay issue was not good," James said. "The people who needed to get paid got paid but it was more the bigger picture. Now we've got our first win and our first clean sheet, it's a much happier place."