The 24-year-old appeared 31 times under prevous Chelsea boss Mauricio Pochettino last season but his position has now been taken up after the club signed Filip Jorgensen from Villarreal.
The Serbian signed a new contract on improved terms at Stamford Bridge before agreeing the loan as he secures his future at a club that looks to develop him.
Chelsea signed the keeper from New England Revolution for £14m last summer who will now help strengthen undefeated Strasbourg as they fight in France's top flight.
American defender Caleb Wiley and Brazil international Andrey Santos are also Chelsea loanees with their French partners.
The club also sold winger Diego Moreira to the Ligue 1 side earlier this month which means four former Chelsea stars will help the French side compete for the title.