Chainrai took control of the club from Ali al-Faraj, who in turn had followed Sacha Gaydamak and Sulaiman al-Fahim.
Chainrai has taken over the 90 percent shareholding in the south coast club that was held by al-Faraj after triggering a clause when he did not receive repayments of a 17 million pounds loan he made to the club via his company Portpin.
"Portpin have implemented the clause with immediate effect," a club spokesman said on Thursday.
"It is a temporary measure. He has lent al-Faraj money to keep the club going and will now come in and stabilise the club before looking for a new owner as soon as possible."
Portsmouth are currently banned from buying players because of money owed to other clubs while the players and staff have regularly had their salary payments delayed this season.
Portsmouth, who lost 1-0 at Fulham on Wednesday to remain five points adrift at the foot of the Premier League, are fighting a winding-up order from the Government's Revenue and Customs department.
They are appealing against the ruling, with a hearing due in the High Court on February 10, when the club could be forced into administration.
