The 31-year old joined his boyhood club from Manchester United on Sunday.
"It's all about his fitness and his desire, but he has shown me that ambition that we need. He knows how to win titles, as I said.
"The Under-20s are World Champions but not in the Premier League. He is that player. And don't forget the experience he will give to the rest of the team.
"Wayne, of course, is still competitive – he will be a competitor always – and he wants to play at the highest level that is possible for him. We have spoken several times about Everton and what we are striving to achieve.
"We have a lot of young players and sometimes in life you need somebody who you look up to, who you learn from.
"That was also one of the messages when we spoke about on and off the pitch what his function will be in the team."
"One of the functions for Wayne is to show the rest of the team why he is - and still is - that player."