The Costa Rica international made just 11 appearances last season as he struggled to recover from a double-break of his leg.
And the 25-year-old then suffered a fractured metatarsal in April, which brought his campaign to a premature end.
Oviedo made his first appearance in five months in a friendly against Scottish Premiership side Hearts at Tynecastle on Sunday.
He suffered no reaction on his return, as Everton continued their preparations for the new season with a 3-1 victory.
“Now everything is coming together well and I hope to play more minutes in this pre-season and be ready for the season ahead,” Oviedo said on the club’s TV channel.
“I hope I can work hard on my fitness and get more minutes in the next game. It was a long wait but now it is in the past. Now the most important thing is to work hard and to be ready.
“For me, the most important thing is the future now.”