The Italian, who left Napoli earlier this month, replaces Portuguese Marco Silva, who was sacked after the Premier League club’s 5-2 defeat by Merseyside rivals Liverpool.
Everton named Carlo Ancelotti, one of Europe's most successful coaches, as their new manager on Saturday, giving the three times Champions League winner a 4-1/2 year contract.
The Italian, who left Napoli earlier this month, replaces Portuguese Marco Silva, who was sacked after the Premier League club's 5-2 defeat by Merseyside rivals Liverpool.
"This is a great club with a rich history and a very passionate fan base. There is a clear vision from the owner and the board to deliver success and trophies," Ancelotti said in a club statement.
"That is something that appeals to me as a manager and I am thrilled at the prospect of being able to work with everybody at the club to help make that vision a reality.
"I have seen from the performances in the last two weeks that the players are capable of so much."
Ancelotti, who has won the Champions League twice with AC Milan and once with Real Madrid, left Napoli after falling out with chairman Aurelio di Laurentis.
The 60-year-old now faces a different sort of challenge in revitalising Everton, who are three points above the relegation zone ahead of Saturday's home game against Arsenal.
Ancelotti previously managed Chelsea, winning the Premier League and FA Cup in his first season in 2009-10, before being sacked after a trophyless second campaign.
He has also won domestic league titles with Italy's AC Milan, France's Paris St Germain and Germany's Bayern Munich.
The Italian confirmed interim coach Duncan Ferguson will be part of his backroom staff at Goodison Park.
"The work Duncan has done is a great credit to him," Ancelotti added.
"Strong organisation, strong discipline and the right motivation are some of the key ingredients in football and I'm pleased that he will be part of my backroom team moving forward."
Everton's director of football Marcel Brands said he was excited to have secured the "perfect appointment" in Ancelotti.
"He is one of the finest managers in world football and a proven winner, having achieved a remarkable level of success in each of Europe's major leagues," he added.
"This was a clear and exciting decision for the board to make. It was a unanimous choice and one we were all fully united behind throughout."
Everton said on Thursday that Ferguson would remain in charge for the Arsenal match. Ancelotti's first game in the dugout will be against Burnley at Goodison Park on Boxing Day.