Grant succeeds Paul Hart, who was sacked due to poor results that saw Portsmouth rooting the league table with seven points from 11 games.
Last month, Grant was appointed as director of football but wasn't seen back then as a potential replacement to Hart.
"Avram is a very experienced and respected manager who has managed at the highest level," said Peter Storrie, Portsmouth chief executive.
"The board believes he is the man to help steer the club out of the relegation zone," he added.
According to a report published by The Guardian, Storrie wasn't a big fan of Grant but the former Chelsea and Israeli national team manager was supported by Mark Jacob, Al-Faraj's lawyer and closest aid.
Portsmouth take on title holder Manchester United on Sunday.