Allardyce has agreed to take over at Goodison Park after the departure of Ronald Koeman last month, and has agreed a deal until June 2019.
"I've always thought Everton was a great club. It is a great club," he said. "Obviously, the club has gone through a difficult spell and hopefully I can put that behind us as quickly as possible and start looking upwards again.
"Last season showed what the club is trying to build and we need to demonstrate that level of ambition and assuredness again. We can. It's a question now of putting in the work to do that and I’m really enthused by the prospect."
The 63-year-old is the fifth-most experienced manager in Premier League history, having taken charge of 488 matches with Bolton Wanderers, Newcastle United, Blackburn Rovers, West Ham United, Sunderland and Crystal Palace.
He has recorded 165 victories at a win percentage of 33.8.
Allardyce arrives at Everton with the club lying 13th, with 15 points from 14 matches.
Caretaker manager David Unsworth, who has been in charge for five matches, oversaw Everton's 4-0 win over West Ham on Wednesday, which Allardyce observed from the stands.
Allardyce's first match as Everton manager will be at home to Huddersfield Town on Saturday.
Everton have confirmed that Unsworth will return to his role as the club's PL2 coach.