Redknapp has been handed a £3million-a-year three-year contract.
He said: “If I can’t keep Spurs up I will quit at the end of the season.”
Redknapp, 61, added: “It is a fantastic opportunity, one I couldn’t turn down.”
Tottenham chairman Daniel Levy has agreed a £5million compensation package with Portsmouth.
Sporting director Damien Comolli and first-team coaches Marco Alvarez and Gus Poyet have also left Spurs.