The 28-year-old has moved to Turkey until the end of the 2019-20 season after falling out of favour under Maurizio Sarri.
Moses was converted from a winger to wing-back by Antonio Conte, Sarri’s predecessor, playing a key role in the 2016-17 title triumph.
The Nigeria international first joined Chelsea from Wigan in 2012 and spent time on loan at Liverpool, Stoke and West Ham before earning a regular first-team spot.
In total, Moses has made 128 appearances for Chelsea, scoring 18 goals across four seasons.
Fenerbahce have also enquired about Moses’ team-mate Danny Drinkwater, who also finds himself down the pecking order at Stamford Bridge