The Costa Rican star has signed a four-year contract and joins the Toffees for an undisclosed fee.
The 22-year-old has been granted a work permit.
Oviedo told the club’s official website: “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.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.