On Friday the club had claimed they were on the brink of ceasing trading because Gaydamak had refused to sign a deal to sell to Balram Chainrai.
But Gaydamak said late on Saturday that a new agreement had been reached.
Balram Chainrai, a Hong Kong-based businessman, became Pompey's fourth owner inside a year when he assumed control of the club in February 2010 before putting them in administration soon after.
"We are very pleased to have finally completed the sale process," added Balram Chainrai.
"We look forward to working with the senior executive team and the football manager, and to be part of the rebuilding process of this historic club."
"We need to stabilise and Levi and I will be taking time to get a closer understanding of the business so that we can ensure the club is taken forward in the right way."
The saga surrounding the ownership of Portsmouth, who won the FA Cup in 2008, began in August 2009 when Gaydamak sold the club to Sulaiman Al Fahim.
Two months later Ali Al Faraj become the new owner when he acquired 90% of the shares from Al Fahim.
Three weeks after that Balram Chainrai lent Al Faraj £17m but the off-pitch turbulence continued as Avram Grant replaced Paul Hart as manager, the club failed several times to pay its players on time and HM Revenue & Customs issued a winding-up order over tax issues.
In February 2010 Balram Chainrai seized the club's assets before placing the club in administration with debts estimated to be about £120m.
The club subsequently had nine points deducted for going into administration, were relegated from the Premier League and in June appointed a new boss in Steve Cotterill.
In August Portsmouth survived an attempt by HM Revenue & Customs to block a Company Voluntary Agreement, which could have prevented the club exiting administration.
As recently as Friday the club claimed it appeared "likely to close" after a row over £2.2m owed to Gaydamak saw talks break down.
We're now in a position where we can look to move forward
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.