Spurs, who made the announcement on their website, finished fourth in the Premier League in 2009/10, Redknapp's first full season in charge at White Hart Lane.
Their highest finish in the Premier League, bringing with it a place in the Champions League qualifiers for the first time, was a triumph for Redknapp who has transformed the club's fortunes since he joined from Portsmouth in October 2008.
When he arrived, Tottenham were bottom of the league after their worst start to a season.
Redknapp's contract had been due to expire in 2011 but included an option for two more years.
The 63-year-old, who won the Premier League manager of the season award, said he could stay for longer.
"I am now committed to Spurs for the next three years, and of course I am pleased by that," he said.
"That has made me think about how long I want to stay in the game and, who knows, I might stay with Spurs many more years than 2013.
"You never know what is around the corner and, while I have the energy, I think I will carry on for as long as I can," added Redknapp, who won the FA Cup with Portsmouth in 2008.
"I have changed my mind and I feel as though I have a good few years left me in yet."
Redknapp cited the examples of Manchester United's Sir Alex Ferguson (68), Liverpool's Roy Hodgson (62) and England's Fabio Capello (64) as examples of managerial longevity in English football.
"None of them are youngsters any more, they are of the same age group, and it is true that there is no substitute for experience in management," he said.
"The game is crying out for stability, and the experienced guys know the job, and for so many now age is not a problem."
