The Spaniard has been able to draft the Republic of Ireland international into his ranks at Everton, with it possible that he could make his Premier League bow against West Bromwich Albion on Monday.
McGeady arrives in English football having spent time in Scotland with Celtic and Russia with Spartak Moscow.
Martinez admits he has been a fan of the 27-year-old winger ever since he burst onto the scene, and tried to sign him during his time in charge of Swansea City and Wigan Athletic.
His efforts were foiled on both occasions, but he has finally been able to secure the services of a creative talent who is expected to slip seamlessly into an Everton side that would appear to play to his strengths.
Martinez said of his McGeady chase: "The first time I saw McGeady was in 2007. It was a derby between Rangers and Celtic and he was special. He was a match-winner, playing with his socks down at that time.
"I love a player who can enjoy a one-on-one situation like him.
"I enquired but we were at Swansea and we couldn't afford him.
"When he went to Spartak for £10million I thought the price was about right for a player of that quality. The scouts, though, have been taking trips out to Russia to watch him.
"I think the first six months he was terrific, played Champions League football with Spartak and did really well.
"But then, as always happens when you go to Russia, you hit a little bit of a difficult period after the first season.
"Since then I tried to get him in every window I could. With Wigan as well. The difference was that he was out of contract in the summer.
"Previously, Spartak had no need to sell. They didn't need the money and they didn't want to lose Aiden.
"Then the player wasn't going to sign a contract, so it was a power struggle.
"If I'm honest with you, I knew he'd come to us in the summer as soon as he finished his contract at Spartak, but I didn't think we would have the opportunity to get him now."