McGeady – who has strong west Donegal connections – joined from Spartak Moscow.
The former Celtic player, 27, has agreed a four-and-a-half-year deal.
He was presented to the crowd at Goodison Park before Saturday’s 2-0 Premier League win over Norwich City.
“It seemed as though we were going to get him in the summer, but with Nikica Jelavic set to move to Hull it was important he could join us quicker,” said boss Roberto Martinez.