The 29-year-old left-back arrived at Old Trafford in 2020 for £18million after a very impressive four-year spell with Porto.
Telles failed to make his mark under both Ole Gunnar Solskjaer or interim manager Ralf Rangnick, and is not in Erik ten Hag's plans.
A club 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."
Meanwhile, Telles said: "To everyone at United: colleagues, staff, fans. I will be supporting and cheering you on all season. Thanks for the moments so far."
The Brazilian was previously linked with a return to Porto, and was a fan favourite during his time in the Primeira Liga.
He netted 26 goals in 195 games for the Portuguese giants, won two titles, and broke into Brazil's national side.
The full-back was an unused substitute in United's 1-0 defeat to Atletico Madrid on Saturday, before starting the 1-1 draw against Rayo Vallecano on Sunday.
United brought in Dutchman Tyrell Malacia earlier this summer from Feyenoord, increasing competition for places in Telles' position.
Malacia will battle with Luke Shaw for a the left-back spot in the starting XI ahead of the new season.
It is also reported Man United are set to listen to offers for Brandon Williams and Eric Bailly.
Phil Jones, who is expected to join Wayne Rooney at DC United, and Axel Tuanzebe are also likely to be moved on in the near future.
The Premier League is back and talkSPORT has it covered, with games on Friday, Saturday and Monday, beginning with Crystal Palace vs Arsenal on 5 August