The former England midfielder beat Monday's transfer deadline to complete his move to Goodison Park alongside Wigan midfielder James McCarthy.
After signing his contract at Everton, Barry told the club's official website: "It's been a long day and the deal was done late but it was something that I always hoped would get over the line.
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"I know all about Everton's history and it's a fantastic club. I've enjoyed playing games at Goodison Park, the atmosphere is always fantastic."
The former Aston Villa midfielder says that he has been keeping an eye on the Toffees ever since he was made aware of Roberto Martinez's interest in his services.
"To be honest, as soon as I heard about Everton's interest I have paid a lot of attention to the opening games," the 32-year-old added. "The bits I've seen, they've been unlucky not to win the games that they drew."
Everton boss Martinez hopes Barry's arrival will help fill the hole left by the departure of midfielder Marouane Fellaini to Manchester United.