Redknapp was named new Tottenham manager on Saturday.
“Harry is a great manager and we, of course, did not want him to leave. We tried everything we could to keep him at Portsmouth,” the chairman told the club’s official website.
“However, he made it clear that although he has achieved great success here at Fratton Park, apparently Spurs is one of the only clubs he would consider leaving for.
“We have subsequently agreed a substantial compensation package with Spurs, although our overwhelming desire would have been to retain the manager.
“On his return to Fratton Park (in 2005), Harry performed a near miracle in keeping us in the top flight and we have since gone on to become an established top ten side. Last season we won the FA Cup for the first time in nearly 70 years and qualified for European competition for the first time.
“Everyone at the club has enjoyed an excellent working relationship with Harry and he has been a very good friend to me personally.
“The last thing I wanted was to see Harry leave this club but the lure of Spurs proved too much for him to turn down.”
Club owner Alexandre Gaydamak added: “I am personally disappointed that Harry has left.
“We did all we could to keep him and up until early evening Saturday I was under the impression that he would be staying as Portsmouth manager.”