The trophy was the first of Redknapp's career and qualified Pompey for Europe for the first time.
Redknapp was arrested in November as part of the investigation into alleged corruption involving transfers and he turned down the vacant managerial job at Newcastle over the winter.
"Harry's on a long contract," Portsmouth chief executive officer Peter Storrie said. "He's here as long as he wants to be here. I think that will be for a long, long while. This is his team. He built this team and wants to take them to the next level. I think he'd go barmy if he packed up. He'd be ringing me up saying: 'Take me back quick."'