The midfielder, who just joined Goodison Park in January, is looking to restart his career in Turkey after finding it difficult to make Frank Lampard’s team.
As they battled relegation last winter, Everton acquired Alli from Tottenham in the hopes that he would regain the form that had made him one of England’s most promising young players.
Alli was no longer considered for the national squad after sliding down the Spurs pecking order.
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Alli, who has 37 England caps, continued to play in 11 games to help the Toffees avoid the relegation, but he failed to score any goals. This season, he has served as a substitute twice.
Now that Everton manager Lampard has given him permission to depart, he has decided to move to Super Lig team Besiktas in order to start again.
Alli arrived in Turkey early on Thursday and was welcomed by hundreds of Besiktas supporters before finishing his physical.