The 27-year-old spells fifth loan since joining the Blues in 2016.
Batshuayi has recently had stints with Borussia Dortmund, Valencia and two spells at Crystal Palace, where he scored two goals in 18 league appearances last season.
The Belgian has not featured for Chelsea since February 2020.
Turkish side Besiktas won the 2020-21 Super Lig and will feature in the Champions League.
Since arriving at Stamford Bridge from Marseille for £33m, Batshuayi has scored 25 goals in 77 appearances for the Blues.
He scored six goals under Frank Lampard in the 2019-20 season but with Tammy Abraham and Olivier Giroud in fine form that season he struggled for opportunities.
He helped Chelsea to win the Premier League in 2016-17, his debut season.
The move comes as Romelu Lukaku returns to the Blues and Abraham departs for Roma.
Ishaq Mustafa
