Pompey chief Steve Cotterill snapped up the 28-year-old Norway midfielder in an initial switch until November 7 and the player should go straight into the squad for Tuesday night's visit of Peterborough.
"He's a central midfielder who can also play on the right side," Cotterill told Pompey's official website.
"He's energetic, a good footballer and has played 31 times for his country. He played on loan for Sheffield United against us last season and did very well.
"We've got several midweek games and we may need to shuffle the pack so he will help us out."
Meanwhile, Ipswich boss Paul Jewell has confirmed that Fulham have not contacted them about ending Stockdale's season-long loan stint at Portman Road, despite Mark Schwarzer picking up a back injury at West Brom on Saturday.
Jewell told his club's official website: "We haven't heard anything from Fulham regarding David.
"Obviously when we heard Schwarzer had picked up a knock we were concerned but, as I said, Fulham haven't been in touch with me.
"We are at the mercy of them a little bit with the 24-hour recall clause and it's not ideal, but it was a chance we were willing to take to bring David here and hopefully the gamble will pay off."