Four years after a bout of food poisoning scuppered their qualification efforts on the last day of the season at West Ham, Spurs secured a fourth-place finish with a game to spare after Peter Crouch's header gave them a deserved victory.
Manager Redknapp will now take his team to Burnley on Sunday knowing that Manchester City can no longer catch them.
Jumping for joy: Michael Dawson celebrates with Danny Rose after Spurs' victory
Redknapp - drenched by a bucket of iced water in the tunnel after the game - said: 'This is great for the club and it's a great feeling.
'We only had two points and were bottom when I came here last season and it took us a long time to get out of it.
'So to be where we are now is fantastic. We have played some great football this season and I think we have been a pleasure to watch. This was a big year for us to do this and it will be great to be in Europe. I thought we were fantastic tonight and we had some superb performances.
Champagne moment: Bentley, Crouch, Pavlyuchenko and Modric
'I thought City were the only club that could break into the top four. I thought we could come sixth or seventh. Happily I was wrong.'
Spurs went into the game knowing that a draw would leave them apoint ahead of City and in pole position going into the final game.
But Redknapp sent out an attacking team with instructions to go for it from the off.
Executive stress: Manchester City chairman Khaldoon al-Mubarak (left) and chief executive Garry Cook in the stands at Eastlands
His side were by far the better team and the only surprise was that it took until the 82nd minute for Crouch to head home the winner. Prior to that, the England striker had hit a post, had a point blank header saved by Marton Fulop while Ledley King had a first-half header disallowed.
'The team I picked was a gamble,' added Redknapp.
'Most teams play with one striker these days but I wanted to play with two and be brave. I'm sure that some people would have looked at my selection and thought I was mad.
'But I wanted to win the game. I have had 1,100 matches as a manager. I wouldn't have survived this long if I was a mug. I would like to think I know what I am doing.'
Barrel of laughs: David Bentley ambushed manager Harry Redknapp
Crouch was run close as man of the match by captain King but the England striker could not contain his joy. He said: 'We have a fantastic squad and we're capable of anything. But for a club like us to break in to the top four is fantastic.
'This is one of the best things that I've ever been involved in and I am delighted.'
Tottenham can still finish third in the league if Arsenal lose against Fulham at the weekend and Redknapp's team win at Burnley.
Uncertain future: Manchester City boss Mancini
City will play in the Europa League and manager Roberto Mancini will face speculation about his own future. Sources at City continue to stress that he will be in charge next season and the Italian said: 'Yes, I will be here. Why not? We have had a good season. The difference at the end was only one point or two points. It's nothing.
'I am disappointed. We did not deserve to lose this game. We were unlucky. I think that next season we will do better.
'I have only been here for five months. I am not a magician. I do not have a magic wand.
'We have done our best and have come very close.'
Mancini arrived in December because City's owners didn't think previous boss Mark Hughes was on course to meet a 70-point target. The maximum points now available is 69.
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