"He is understood not to be interested in a long-term ownership, just averting the current crisis," said BBC sports news correspondent Gordon Farquhar.
A Pompey spokesman stated: "Portpin (Chainrai's company) have exercised a clause in their contractual agreement to take a controlling interest. They are taking control on a temporary basis to allow new owners to be found.
"Portpin's aim is to come in and stabilise the club, sort out the business with the winding up order from HM Revenue and Customs and sell it on to new owners."
Portsmouth chief executive Peter Storrie previously admitted his position at the cash-strapped club was "probably" untenable after learning that transfer deals were being done behind his back.
However, Storrie will retain his position under the club's new ownership.
"New directors will be appointed to the board and Peter Storrie will remain as chief executive and will be running the club," said a Portsmouth spokesman.
Pompey have lurched from one crisis to the next in recent months, with the Premier League club facing a winding-up petition from HMRC at the High Court on 10 February for unpaid taxes.
They have also been late paying wages four times this season, while Storrie appeared before a crown court accused of tax evasion in January.
Now Chainrai, 51, has taken charge after his company took over Al Faraj's 90% shareholding in the south-coast club.
"Chainrai has invoked a clause in a loan contract he struck with the club's third owner this year, Ali Al Faraj, giving him the right to take over 90% of the shares should they default on repayments to him," added Farquhar.
"He recently loaned the club £15m to £20m to help get them through their current financial crisis, which still isn't resolved.
"Now the loans have not been repaid, he's the new owner of the club."
Had Chainrai simply stood back and allowed Portsmouth to founder and enter liquidation, he would have lost the money he had invested.
"That's the real risk for them, so they need to keep the club afloat by doing whatever they can," added Farquhar.
Chainrai's loans were secured against Al Faraj's 90% shareholding, Fratton Park stadium and future TV revenue.
The businessman told the Portsmouth News newspaper: "Portpin has made substantial loans to Portsmouth to try and ensure the club's future. Portpin will continue to work for the best interests of the club."
Meanwhile, Pompey manager Avram Grant said he will continue to try to save the Premier League strugglers but remains non-committal about his long-term future.
The club remain rooted to the bottom of the table after a 1-0 defeat by Fulham on Wednesday.
Key players Asmir Begovic and Younes Kaboul were sold against Grant's wishes in January.
But Grant stated: "As long as I am here, I will keep fighting."
As well as the delays in paying player wages, Portsmouth have debts of £60m.
But, for the moment, Grant is committed to trying to keep Portsmouth in the top flight, with a trip to Manchester United the next challenge on Saturday.
"I think that we need to do our best all the time and, as long as we have a chance, we have to fight," he added.
"It's very hard times off the pitch but I'm very proud of the players. I think if everything was a little bit more calm the results would be even better."
Pompey and England goalkeeper David James told BBC Radio 5 live of the "frustration" felt by the players.
"You try and tell the lads that you do get paid even if it's a week late, 10 days or whatever - we are getting paid one way or the other," said James.
"We're not sure if we've got anyone else to sell to get paid.
"The fact is we do get paid and there are other clubs with players who aren't getting paid and historically there have been other clubs that players haven't got paid, so it could be worse."
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