The left-back has joined former club FC Copenhagen, signing a contract that will run until 2022.
The terms of the departure have not been revealed, though a statement on the FC Copenhagen website said that he joined after being ‘released’ by Sunderland.
As the biggest earner at the club by a significant margin, Sunderland were keen to find a solution to take his wages off the bill.
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A club statement from Sunderland reads: “Sunderland AFC can confirm that Bryan Oviedo has joined FC Copenhagen.
“The left-back, who moved to Wearside from Everton in January 2017, returns to the Danish Superliga side seven years after departing following a two-year spell at the Parken Stadium between 2010 and 2012.
“SAFC would like to thank Bryan for his service to the club and wish him all the best for the future.”
Oviedo made 77 apearances for the Black Cats.
Copenhagen boss Stale Solbakken praised Oviedo for making the deal possible.
“He is a defender with great offensive qualities, but at the same time he knows what is expected defensively and we have full confidence that he can complete the task.
"The economics made it difficult, but he himself invested in the fact that it was possible. It is good to see a player that will optimize their career sportingly and not look at it in the short term financially, and we are of course very pleased that it has now succeeded.”
Meanwhile, Stewart Donald has told supporters that Jon McLaughlin will not be sold this summer.
The 31-year-old has one year left on his current contract, and his stellar performances last season drew interest from other clubs.
Millwall were heavily linked after their move for Ipswich goalkeeper Bartosz Bialkowski fell through. There was also reported interest from abroad, with Trabzonspor, Qarabag and Ludogorets said to be keen on a move.
Sunderland are now keen to secure an extension, after bringing a swift end to similar speculation over Aiden McGeady’s future earlier this summer.
Donald spoke to supporters at a special Q&A before the final pre-season friendly against Heerevenveen, hosted by the Wise Men Say podcast.
“The scenario is, Jon has got a year left, he’d love to extend [his contract],” Donald said.
“He’s very happy here.
“We spoke to his agent and have begun that process. His agent said there is interest in him, you could probably get £1 million or £2 million for him.
“I said, ‘would you get £5 million?’. He said, ‘no chance’.
“So I said, ‘well that’s his price then’.
“So will Jon McLaughlin be here all season? Yeah.
“We won’t sell Jon McLaughlin.”
Manager Jack Ross is keen to secure McLaughlin’s future, highighting his importance earlier this summer.
“From a football point of view, I've no interest in Jon not being at the club,” he said.
“I've said before about him being high quality, low maintenance. There's not many like that.”