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 [ Images ] 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 [ Images ] replaced Mark Hughes as City manager. He had a loan spell at Real Madrid [ Images ] 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 (www.tottenhamhotspur.com):
"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."