Chelsea confirmed the transfer on their official website but are yet to disclose the financial details of the transfer.
The Blues have been on the look-out for a new left-back following Felipe Luis’ return to Atletico Madrid earlier this summer.
Sky Italia reporter Gianluca Di Marzio recently reported that Chelsea were interested in Telles.
Telles was part of the Galatasaray side that won the league title for a record 20th time last season. The Lions also won the double and earned the right to wear a fourth star on their shirt next season.
The 22-year-old joined Galatasaray on a €6 million transfer from Gremio last January and still has another three-years left on his current deal. Telles provided a total of two goals and three assists in 56 games for the Lions last season.