There had been speculation the 27-year-old Irishman would sign a pre-contract agreement with the Toffees but he will move to Merseyside immediately having agreed a permanent deal.
McGeady was paraded to supporters at Goodison Park prior to their Barclays Premier League game against Norwich.
McGeady has signed a four-and-a-half year deal with the Merseysiders after the clubs agreed an undisclosed fee.
McGeady spent six years with Celtic before moving to Russia for B£9.5million in 2010.
The news sees Goodison boss Roberto Martinez finally land his man having been linked with him while at Wigan a year ago.