And after a disappointing season which saw Charlton finish 19th to go back into The Championship, Hreidarrson has used the clause to move to The South Coast.
He has signed a two-year deal with Pompey, who finished 9th in The Premiership this season under Redknapp.
"I've always had a lot of respect for Harry," Hreidarsson told BBC Sport. "I nearly joined him four years ago at Pompey before I signed for Charlton.
"It was a tough call not to go then and I'm delighted to have a second chance."