Redknapp, 64, is in "excellent spirits" and is due to be discharged from hospital in the next 48 hours, according to Tottenham.
Spurs chairman Daniel Levy said: "We are delighted the operation went so smoothly and successfully."
Levy added: "Knowing Harry he will want to rush back, but it's important that he only does so when he has recovered properly."
Levy said Redknapp had asked for his thanks to be passed to fans who had sent goodwill messages.
Tottenham confirmed on Tuesday night that the former West Ham manager was set to undergo a "medical procedure" that would rule him out of the club's trip to Rubin Kazan this week.
Assistant manager Kevin Bond and first-team coach Joe Jordan will take charge of the team for Thursday night's Europa League match in Russia.
Redknapp lives in Bournemouth and makes the 250-mile round trip to the club's training ground most days along with Bond. The former Portsmouth manager, who has been in charge of Spurs for three years, admitted in March 2010 that he had started talking heart pills upon the advice of his doctors, but stressed it was not a major problem.
Writing in his Sun column, Redknapp then said: "About a year ago I needed to take heart pills and I am still taking them regularly... I am absolutely fine and have no worries about my health but this game can make the most mild-mannered of people explode as when you are sitting on the bench you get eaten up inside from first to last whistle."
On the stresses of management he added: "After a game I cannot sleep, there is too much going on in my head as I go over moves, think about game plans, think about which player has had a good or bad game - and it's worse if you lose."
Source: PA
Source: PA