ESPN reported on Wednesday that United were set for a defensive clearout and Telles is the first to leave the club.
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Following the announcement, Telles posted on his social media account: "Come on! I feel honoured by this opportunity.
"I cannot wait to get the best possible results for Sevilla. I can't wait to make my debut and help my teammates."
Telles moved to Old Trafford in October 2020 and has made 50 appearances in all competitions, scoring one goal.
Anthony Martial also spent a short spell on loan at Sevilla last season but failed to find consistent form.
A United statement read: "A popular and professional member of the squad, Telles leaves United with everybody's best wishes for the campaign to come and Reds supporters will be following Sevilla's results from afar."