The Costa Rican has been a regular starter for FCK after joining from Deportivo Saprissa in his homeland.
The 22-year-old can operate at left-back and on the left side of midfield.
Oviedo told evertontv: "I am so very happy. This is a very good opportunity for me.
"The last two or three days have been very stressful and tiring but I am so happy now. I am feeling good and right now everything is positive.
"I know a lot about Everton. I watch Everton games and Premier League games on the TV and it is a very good league."
Everton have also signed Kilmarnock winger Matthew Kennedy for a nominal fee.
The 17-year-old has agreed a three-year deal with the Barclays Premier League club, after impressing in the Clydesdale Bank Premier League.
Kennedy, who made his debut against Hibernian at the age of 16, has represented Scotland at under-15 and under-16 level.