كتب : Ahmad Saied
Al-Fahim will keep a minority 10% of the stakes and will remain as club chairman for two more seasons.
The title is honorary and Al-Fahim will have no say in how the team is run.
The buyout will have an immediate effect on the squad, with players receiving September's late wages this week.
Al-Faraj had a bid to buy Portsmouth in August turned down and Pompey's chief executive Peter Storrie voiced his delight with the takeover.
"Naturally, I am delighted because I have backed Mr. Al-Faraj's bid initially," he said in a statement carried by the club's website.
"Ali is a passionate follower of the Premier League and wants Portsmouth to remain in the best league in world football."