The Costa Rica international's acquisition was only confirmed after Toffees manager David Moyes had attended a work permit hearing in London on Friday.
And the 22-year-old, whose arrival in training is set to be delayed as he flies out to take part in two World Cup qualifiers this week, revealed his joy at sealing a move.
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“Now I am feeling good, I am happy with everything. I knew that sometimes Everton were watching Copenhagen games but not especially to watch me.”
The former Saprissa man also underlined his versatility, insisting that he is willing to play anywhere for his new boss David Moyes.
“I am a player who likes to attack,” he added. “I can help in attack but also in defence as well. I can play both positions [left-back and left midfield].
“I played many years as left-back, now [more recently] I have been playing further forward.”
Oviedo went on to admit that he would be joining up with a squad he has watched intently from afar, adding: “I know a lot about Everton.
“I watch Everton games and Premier League games on the TV and it is a very good league.
“I need to come here and work hard for a place. I know there are very good players and I will need to train very well to have a chance of getting in the team.”