Oviedo, who can play as a left-back or as a left-midfielder, has also thanked the Everton fans for their support.
Everton have endured a disappointing season in the Premier League and have finished outside the top 10.
Roberto Martinez parted company last week, and the Toffees are on the lookout for a new manager to succeed the Spaniard.
There are some very good players in the current Everton squad, such as Romelu Lukaku, John Stones and Ross Barkley, but as a team they underperformed throughout the campaign.
Things can only get better next season, and the Everton fans will hope that a new manager is appointed soon.
In 14 Premier League appearances for Everton this season, Oviedo created 13 chances, had a pass accuracy of 81% and a shot accuracy of 75%, and won two headers, eight dribbles and 34 tackles.