The Spaniard was unveiled to the media at Goodison Park following confirmation that he would replace David Moyes.
"This is a really special day to come to Everton Football Club. The feeling already is one of excitement and honour," said Martinez.
"I want to thank the Chairman and the Board for giving me this opportunity. This is a phenomenal and passionate football club, and I can't wait to start.
"It's been a phenomenal time at Wigan, and I enjoyed every second of it, but after four years it was the right time.
"After I met the Chairman, I knew that Everton was the right football club so it has been a natural transition. It's the right time now to be involved in such an exciting challenge."
Martinez accepted that following David Moyes would not be easy and that there would be pressures with the job.
"It's a huge pressure, but I'm extremely proud of that pressure," he added. "David Moyes has set real standards over 11 years, and what he has produced is a platform for the next man to continue.
"I feel fortunate that I am able to carry on that work he's done He has given Everton an identity and set incredible standards. I want to be humble enough and hard-working enough to take that magnificent job onto the next level."
Martinez was also keen to stress that he is looking to carry on the team spirit instilled by Moyes during his 11 years at Goodison Park
"I hope we can be a really strong unit, from the fans to the board, the chairman, the football staff and the players. We need to become that unit, it's difficult when you break that but it's the right time.
"I believe that Wigan have a great future, it was the right time to have a fresh energy around the place. I'm excited, and I'm looking forward to how quickly we can become a strong and winning unit on the football pitch at Everton.
"I want to meet everyone at Everton, and make sure we get a really strong team. There's going to be a large amount of my back-room staff who are going to come with me.
"The Chairman hasn't put any pressure on me - he says that he wants to get into the Champions League! It was quite simple to take the job. The fans need to know they are the most important part of this football club and we will need them.
"We can carry on looking to achieve more. Finishing in the top six was a magnificent achievement for Everton and we need to carry on building if we want to improve on that."