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.
Martinez later revealed the club had been discussing terms with McGeady for next season when an opportunity arose to sign him immediately arose.
The Toffees boss said: "Full credit to the chairman and the board.
"We were talking to Aiden and we agreed for him to come next season.
"But because of his situation in Spartak, obviously that he wasn't going to be involved too much, and the situation with Nikica Jelavic, we were quite happy to make it happen now.
"I do feel the money we are going to spend will be well spent.
"In a matter of hours it fell into place.
"I was delighted to have Aiden at the end of the season but now it is a real boost to be able to work with him straight away."