The former Wigan boss has been announced as the successor to Manchester United-bound David Moyes, signing a four-year deal after leaving the DW Stadium.
Martinez won the FA Cup with Wigan in May, beating Manchester City in the final, before seeing the Latics relegated following eight years in the Premier League.
The 39-year-old was approached by Aston Villa to replace Gerard Houllier in June 2011, before holding talks with Everton's city rival Liverpool 12 months later, but rejected a move after refusing to share control of recruiting players.
"This is a real, real special day," Martinez said. "And I have this feeling already of excitement, honor. This is a phenomenal and passionate football club and I can't wait to get sunk with everything it means (to be) at Everton and make sure we start working on playing football to be extremely proud (of)."
Martinez replaces new Manchester United boss David Moyes at Everton.
"Almost his first words to me were, 'I'll get you in the Champions League,'" Everton owner Bill Kenwright said, "and that is extraordinary for a man who doesn't know much about the football club from the inside but who has obviously studied the football club and looked at what we have been doing the last few years.
"I'm not going to say to you that it was like David Moyes and he got me in 30 seconds — it took him at least 45 seconds. He understands the game, he understood Everton, the history, all the players, what he wanted to do ... All I can say is, when you know, you know."