Chilwell, 28, has been unwanted at Chelsea since the appointment of Enzo Maresca at the start of last season.
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The England international spent the second half of last season on loan at Crystal Palace, where he only managed to make 11 appearances across all competitions, scoring one goal.
Chelsea have now confirmed that the left-back has joined BlueCo sister club Strasbourg on a permanent basis, ending his five-year tenure.
The transfer fee the Ligue 1 side paid Chelsea is as of yet unknown, but it has been confirmed that Chilwell has signed a two-year contract.