The 24-year-old featured in 31 matches under former Chelsea manager Mauricio Pochettino last season, but his spot in the squad has been filled following the arrival of 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 and will welcome the keeper into the club this summer.
The club also sold 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.