Hreidarsson is set to sign for first division table-toppers Portsmouth, while Ambrose is in talks with Bobby Robson about a possible move to the Premiership with Newcastle United.
Town Chairman David Sheepshanks told the clubs website: "These sales were a necessity in our current situation and the matter was largely out of our hands.
"Supporters will be disappointed about the need to sell when we are so close to the play-offs.
"No matter how much we wish it were different, regrettably financial institutions only work on certainty and not on hope value.
"We still have a strong team and we all hope that in the face of this adversity we can still challenge for and gain a play-off place."
If both Town players agree personal terms with the respective clubs, their transfers are expected to be completed early next week.