The 36-year-old veteran is currently on international duty with Iceland but will put pen to paper on the deal when he returns to the south coast.
Hreidarsson has not played since rupturing his Achilles tendon against Tottenham in March, but will play behind closed doors for his country against an under-23 side in a friendly on Thursday.
He could play a part in Iceland's Euro 2012 qaulifier against Portugal on Tuesday to mark his comeback, but Pompey boss Steve Cotterill was delighted to have secured his services for another season.
"The contract has been agreed and ran from Wednesday. It can be signed when Hermann comes back," Cotterill told the Portsmouth News.
"We are just hoping he is going to come back and be the player he was before he was injured.
"Should he do that - which we have no doubts - he will be a really good addition to our squad.
"He was going to play in a behind-closed-doors game over in Iceland today against an under-23 team.
"We'll see how he gets on, have a chat with the Icelandic national coach afterwards and then have a conversation as to whether he will play in our game at Farnborough on Monday.
"I think Hermann being involved in their game against Portugal on Tuesday is a little bit early but he is a determined so-and-so.
"In my opinion, though, I don't think he is ready for that yet.
"However, the chances are they would want him around for motivational purposes.
"We will wait and see. As long as he stays fit and clear of any injuries we will be delighted."