Sources told ESPN earlier this month that Benitez was in talks to take charge at Goodison Park but faced competition from Roberto Martinez, Eddie Howe and Nuno Espirito Santo for the vacant position.
"You can see the ambition is there," Benitez told Everton TV. "This club is growing.
"For me, it is about bringing the winning mentality, being competitive, so everything is in place on the pitch and off the pitch. I love the passion of the people behind the club. I know the city, I know Scousers, I know what it means for every fan here to compete and to have the chance to win.
"To come to Everton is something that means a lot, for sure. You can see the ambition of the owner, of the board, everybody wants to be better and to go to the new stadium with a massive boost. I like to compete. I like to win. I came from the academy at Real Madrid [as a young player and coach], and the winning mentality is already there.
"We [Benitez and the coaching staff] have won 13 titles because we have this mentality and I still want to win. And I have come to Everton because I liked the idea to be competitive again -- and to have the chance to compete in every game, to compete against anyone."
Everton's majority shareholder, Farhad Moshiri, added: "Rafa impressed us greatly with his knowledge and experience but, above all, the passion and hunger he showed to join our club. We are appointing Rafa because we believe he will bring success to our Club and to Evertonians.
"To put it simply -- we need to be competing at the top end of the league and to be winning trophies. Rafa is a proven winner with huge experience in coaching internationally and we have secured the best man to achieve that for us."
During his time at Liverpool, Benitez described Everton as a "small club," but he has since claimed that his remarks were misinterpreted.
It is not the first time Benitez's appointment has caused controversy after he temporarily took charge of Liverpool's rivals Chelsea in 2012.
The Spaniard has been out of work since leaving Chinese team Dalian Professional in January.
Everton will be hopeful Benitez can help the club lift their first major trophy since 1995.