"Sulaiman al-Fahim welcomed this agreement and looks forward to helping the club build on its impressive history and achieve new successes in the Premier League," the club said in a statement on its website.
Portsmouth announced on July 21 that an agreement in principle had been reached to sell to Al-Fahim.
However, delays in finalising the deal prompted the formation of a new consortium led by chief executive Peter Storrie try to buy the club last week.
'Fit and proper'
Al-Fahim was named Portsmouth chairman after passing the Premier League's "fit and proper" test for prospective club owners last month.
He fully owns Al Fahim Asia Associates Ltd, the company that has bought Portsmouth making him the sole owner of the south coast club which won the FA Cup in 2008.
A board member of the Abu Dhabi United Group for Development and Investment, Al-Fahim fronted the bid from Sheikh Mansour bin Zayed al-Nahyan for Manchester City last year.
Portsmouth, without a point from their first three matches this season, have been forced to sell a number of their best players to reduce debts.
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