The current badge was condemned by supporters after the motto 'Nil satis nisi optimum' was removed and the Toffees were forced to apologise in May for not consulting more widely on the redesign.
Everton restarted the process over the summer and an online poll, giving a choice of three options for next season, voted overwhelmingly in favour of a return for the motto.
"I was impressed straightaway when I saw it but there has been a huge majority of fans (78% of 13,229 respondents) have chosen this one," said Martinez after unveiling the new crest.
"It captures what we were looking for: to have a modern touch and to be a global badge without taking away all the key icons of the football club.
"Certain icons represent many years of history and that is important: fans made it clear they wanted to see the tower and our motto and I think it is important 'Nil satis' is back on the badge.
"It has been terrific work from the club as it was important to come up with something which pleases everyone."