Adebayor, 28, spent last season on loan at White Hart Lane from City and scored 18 goals in 37 appearances to finish the campaign as the London club’s leading scorer.
Spurs did not reveal how much they had paid to secure Adebayor’s services but reports in the British media claimed the transfer fee was £5 million ($7.9 million, 6.3 million euros).
“I am pleased to be signing for Spurs on a permanent basis after finally agreeing my departure with Manchester City,” Adebayor told the club website.
“It may have taken longer than expected but I am delighted to be back at Tottenham Hotspur. I really enjoyed my time here last season and I am hoping we can achieve great things together again.”
Adebayor is new Tottenham coach Andre Villas-Boas’ third summer signing after Icelandic midfielder Gylfi Sigurdsson joined from German club Hoffenheim and Belgian centre-back Jan Vertonghen arrived from Dutch giants Ajax.
Beaten 2-1 at Newcastle United in their opening game of the new Premier League campaign, Spurs had started the 2012-13 season with Jermain Defoe as their only recognised senior striker.
Russian international Roman Pavlyuchenko left to join Lokomotiv Moscow in January, while experienced Frenchman Louis Saha was released in June and has subsequently joined Sunderland.
Adebayor arrived in England in 2006, joining Spurs’ arch rivals Arsenal from Monaco and spending two and a half years with the club before moving to City in 2009.
He also spent time on loan at Real Madrid in the second half of the 2010-11 season.