The midfielder was this summer expected to leave Anfield having made less than 30 appearances for the club since being signed for £20million in the summer of 2009.
Injuries and an apparent failure to adapt to the Premier League saw the former Roma star loaned to both Juventus and AC Milan.
And Aquilani, who had been signed by ex-Liverpool boss Rafa Benitez as a replacement for Xabi Alonso, had wanted to return to Italy.
He has now got his wish and has moved to Fiorentina on a reported three-year contract, although Liverpool have revealed no details.
A statement on Friday on their official website read: “Liverpool Football Club can today confirm that Alberto Aquilani has completed a permanent transfer to Serie A side Fiorentina.
“The Italian midfielder joined Liverpool in 2009 but made just 28 first-team appearances having spent the last two seasons on loan in his homeland.
“Everyone at the club would like to wish Alberto all the best for the future.”
Fiorentina co-owner Andrea Delle Valle had earlier announced a transfer had been agreed for Aquilani, as he told Sky Sport 24: “Aquilani is ours.”