The 26-year-old joined Everton from Tottenham in February and started one game in 11 appearances for the Goodison Park club last season.
He has made two substitute outings - in league defeats against Chelsea and Aston Villa - for the Toffees this season.
Alli won the last of his 37 caps for England in 2019.
Besiktas have said they will not pay a loan fee to Everton but there is an option to buy included in the deal.
Alli will be paid a guaranteed 2m euros for the loan plus a maximum of 10,000 euros per game.
A two-time winner of the PFA's Young Player of the Year award, he did not score or register an assist in 13 games for Frank Lampard's side.
Besiktas finished sixth in the Turkish Super Lig last season.
News ID : 1174