Hart was axed on Tuesday after winning just two of his 13 league games at the helm and director of football Grant was widely expected to step into the breach.
The 54-year-old former Chelsea manager returned to Fratton Park in October in an advisory capacity.
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However, his return to management mirrors the scenario which unfolded at Stamford Bridge two years ago when he stepped in following then coach Jose Mourinho's decision to leave.
"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 told Pompey's official website.
"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."
Grant, who has been awarded a work permit to take charge of the first team, will be in the dugout for the first time when Pompey host Manchester United on Saturday.
Source: DSG
