Martinez, who has forged a reputation for making the best of limited resources and playing attractive football, has signed a four-year contract to succeed David Moyes, who has taken over from the retired Sir Alex Ferguson at Manchester United.
"It is a real, real special day to come to Everton Football Club and I have this feeling already of excitement, of honour," Martinez told a news conference at Goodison Park.
The Spaniard is likely to bring a fresh approach to the Merseyside club who are used to Moyes's more pragmatic style.
"When David [Moyes] first came to see me 11 years ago, we were in a bad state, his first words were: 'You're not going down'. Roberto, almost his first words were: 'I'll get you in the Champions League'," Kenwright told the news conference.
"And that is extraordinary from a man who doesn't know much about the football club from the inside but [he] had obviously studied the club, looked at what we had been doing over the last few years, has obviously recognised the massive achievement David Moyes has made."
Wigan upset 2012 Premier League champions Manchester City in last month's FA Cup final at Wembley but Martinez could not prevent them being relegated from the top flight days later.
Martinez was heavily linked with a move to Liverpool last year and was even photographed talking publicly with the club's owner John W Henry but has now joined their rivals Everton.
"It's simple, it came in a natural way," he said. "After four seasons it was the right time [to move] and after meeting the chairman I knew Everton was the right football club."
