The midfielder joined the Toffees from Wigan Athletic on transfer deadline day earlier this week.
The Republic of Ireland international told the club's website: "It's things you dream of as a young kid, playing at big stadiums like Goodison. I can't wait to get out there but I know that it's going to take time to establish myself and get into the team.
"I'm going to need to work hard on and off the pitch and hopefully I can get into the team as soon as I can.
The 22-year-old cost Everton £13m.