Redknapp and agent Paul Stretford held talks with Spurs chairman Daniel Levy on Wednesday.
Redknapp had 12 months left on his contract at White Hart Lane.
The former Portsmouth boss was unhappy that Levy had failed to offer him a new three-year contract.
Levy told the club’s official website: “This is not a decision the board and I have taken lightly.
“Harry arrived at the club at a time when his experience and approach was exactly what was needed.
“This decision in no way detracts from the excellent work Harry has done during his time with the club and I should like to thank him for his achievements and contribution.
“Harry will always be welcome at the Lane.”
Redknapp added: “I have thoroughly enjoyed my time at Spurs and am proud of my achievements.
“I have had a fantastic four years with the club, at times the football has been breath-taking.
“I am sad to be leaving but wish to thank the players, staff and fans for their terrific support during my time there.”
