"It has sort of been a long time coming," McGeady told the club's website (www.evertonfc.com). "There was talk over the summer that something might happen, but I am just delighted that it's done and dusted now.
"I have said for a long time now that I wanted to try myself in the Premier League. Now I have a big chance at a great club, under a good manager. I couldn't be happier. It's a dream move really."
McGeady, whose contract with the Russian club was due to expire at the end of the season, joined Spartak from Celtic in 2010, helping them become league runners-up in 2011-12.
He will join up with Ireland team mates Darron Gibson, James McCarthy and Seamus Coleman at Everton.
McGeady, who has Champions League experience, will help Everton's push for a top-four finish and a spot in next season's edition of the elite European club competition.
"I was close to joining the manager a year ago when he was at Wigan," McGeady added.
"He has obviously come here and proved a lot of people wrong. He plays football the right way and got a few good results along the way. I just want to play for a big club like this and I am relishing the challenge."
(Reporting by Sam Holden; editing by Josh Reich)
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