The Portuguese winger, 24, initially joined Celtic on loan from Benfica in 2021 before Celtic signed him on a five-year deal last summer.
He contributed 28 goals and 26 assists in 83 games over two years in Glasgow and had been heavily linked with a £25m move to Al-Ittihad in recent days.
Last week, Celtic signed winger Marco Tilio, 21 from Melbourne City.
Brendan Rodgers has also signed midfielder Odin Thiago Holm from Valerenga since returning to Celtic to replace Postecoglou as manager.
Jota scored Celtic's last goal in the 3-1 Scottish Cup final triumph over Inverness, ensuring the club completed a fifth domestic treble in seven years.
The Portugal age grade international was a key member of Ange Postecoglou's side, picking up all but one of the six Scottish trophies on offer during his tenure.
Jota averaged a goal or assist every 111 minutes, but follows manager Postecoglou and the retired Aaron Mooy in leaving Celtic this window.
And he joins fellow new signings Karim Benzema and N'Golo Kante at Al-Ittihad.
-- Courtesy of BBC Sport