The Togo international scored 18 goals in 37 appearances for Spurs last season on loan at White Hart Lane.
The clubs were reported by British media to have agreed a deal last month for the 28-year-old, who had been earning about 170,000 pounds a week at City.
No financial details of the transfer fee were available but media reports put its value at five million pounds.
Adebayor joined Tottenham's north London rivals Arsenal from Monaco in early 2006 and moved to City in 2009 in the first wave of big-money signings by the Manchester club's Qatari owners.
But he fell out of favour when Roberto Mancini replaced Mark Hughes as City manager. He had a loan spell at Real Madrid in early 2011 before joining Tottenham for the 2011/12 campaign.
"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. I really enjoyed my time here last season and I am hoping we can achieve great things together again."
