The Republic of Ireland international has penned a four-and-a-half-year deal at Goodison Park after an agreed Bosman move at the end of the campaign was brought forward.
Nikica Jelavic's impending sale to Hull City funded the move, with Martinez confirming he is happy for the striker to leave as he seeks a place in Croatia's FIFA World Cup squad.
"Full credit to the chairman and the board," Martinez beamed. "We were talking with Aiden about next season and agreed for him to come at the end of the season.
"Then, because of his situation in Spartak, that obviously he wasn't going to be involved too much and the situation with Niki Jelavic agreeing terms with Hull, we were quite happy to make it happen now.
"I spoke to Niki this morning and he feels this is what he needs.
"I do feel that the money we're going to spend will be well spent."
Jelavic's departure leaves Martinez with loanee Romelu Lukaku as his only out-and-out striker.
However, while the Spaniard will look for an additional frontman, he believes McGeady's arrival will ease the goalscoring burden.
He added: "As you can imagine it's a real boost to be able to work with him (McGeady) straight away, even if there will have to be an adaptation period because he hasn't played much in the last five or six weeks.
"You look at our squad and I've got a couple of people who can play centrally, not necessarily as a number nine like Rom.
"Kevin Mirallas and Steven Naismith can play that role, so (signing) Aiden McGeady doesn't put the pressure on having to bring a number nine straight away.
"We're going to keep looking to see what the best possible situation is there."
