The South Coast club had said on Friday night they were likely to be closed down after Gaydamak "moved the goalposts".
Andrew Andronikou, the club's administrator, played that down and a lawyer representing Gaydamak refuted claims he was asking for £2.2million to be paid up front rather than in instalments over five years.
Gaydamak said he was prepared to sign the deal to sell his share in the club, and that the delay was because of changes requested by the club.
"I fully intended to sign the deal on Friday and had it not been changed at the last minute I would have," he said.
"Everyone understood on Friday that further negotiations were now required. A new agreement was reached late this evening [Saturday] and as soon as I receive the papers I will sign them.
"I hope this draws to an end this unfortunate uncertainty surrounding the club. I wish everyone involved in the club well for the future."
The club confirmed on Saturday evening that the sale had been completed and were no longer in administration.
Pompey continued their resurgence on the pitch on Saturday afternoon with a 2-1 win at Hull City.
Steve Cotterill, the manager, said there was never any doubt of the club pulling out of the fixture at the KC Stadium.
"We agreed that for the sake of our fans, Hull City and football, even if something was going to happen to our club overnight, we had a duty to turn up and play the game," he said.
"It has been difficult. It was quite big news on Friday night. There were a lot of people worried about their careers. Not just players, but people like our media guys, masseurs and coaches.
"It's a great club. It's got into bad waters through its own fault. We got into this situation, it's no one else's fault. But we would like a break and we would like a go at getting out of it. That's not going to happen overnight. We are trying to do it properly, but I think a lot of neutrals are rooting for us."