The Holland striker has signed a three-year contract with the Turkish giants, the club confirmed on their official Twitter account.
The 31-year-old, who moved to Anfield from Feyenoord in 2006, found first-team starts hard to come by under Kenny Dalglish last season.
Kuyt, who had a year to run on his Anfield contract, had been expected to leave Merseyside this summer, despite the departure of Dalglish, after a season in which he scored just two Premier League goals.
He claimed last week he had attracted interest from a host of clubs across Europe.
He was strongly linked with Hamburg and a return to Feyenoord, although he ruled out the latter, saying they would not be able to afford his wages.
He has opted for a move to Istanbul, though, possibly attracted by the prospect of Champions League football next season.
Fener will enter the preliminary rounds of the competition after finishing runners-up to Galatasaray in the Super Lig.
Kuyt leaves Liverpool having won just one trophy in six seasons on Merseyside, the Carling Cup last season, when he scored in the penalty shoot-out win over Cardiff.
Liverpool confirmed on their official website that Kuyt had told them he had agreed a move to Fener and the transfer would be complete in "the next few days".
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A club statement said: "Everyone at Liverpool Football Club would like to wish Dirk all the very best for the future and thank him for his contribution to the club."
The Dutchman, who is currently preparing for Euro 2012 with Holland, scored 71 goals in 285 games for the Reds.
He was never as prolific at Anfield as he was during his time in his homeland, although he was often played out wide.