The American veteran was out of contract this summer and Spurs have beaten off reported competition from both Liverpool and West Bromwich Albion for his signature.
"Brad is a top goalkeeper of real quality who has great experience," manager Harry Redknapp told the club's official website.
“It is good to have three such experienced top goalkeepers at the club in [Heurelho] Gomes, Carlo [Cudicini] and now Brad and it means we have competition for places, particularly with the number of games we will hopefully face next year both domestically and in Europe as well."
Friedel’s agent Tony McGill confirmed the move on skysports.com, saying: "Yes, I can confirm Brad has chosen Spurs, but it was a very difficult decision to leave Villa.
"Brad has really enjoyed his time there, the fans and staff have been exceptional, especially [Villa chief executive] Paul Faulkner, and I know Brad will wish Villa nothing but success.
"But Brad felt the time was right to move on, and he has not been short of offers. The last 48 hours have been hectic.
"Brad is now looking forward to moving to Tottenham and pushing for a starting place and helping them back into the top four next season."
Villa confirmed the move on their website with chief executive Faulkner stating: "I would like to thank Brad for the terrific contribution he has made at Aston Villa in his three seasons here."
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