The former Burnley boss comes in as a replacement for Frank Lampard, who was sacked last week after less than a year in charge.
Dyche had been without a club since he was sacked by Burnley in April last year.
A 2-0 loss to fellow strugglers West Ham United in their last game saw the Toffees sink to 19th position on the Premier League table.
Everton have only recorded three wins from 20 top flight games this season.
Their last victory came against Crystal Palace in October and they have also been knocked out of both domestic cup competitions.
Dyche told the club's official website: "It's an honour to become Everton manager. My staff and I are ready and eager to help get this great club back on track.
"I know about Everton's passionate fanbase and how precious this club is to them. We're ready to work and ready to give them what they want. That starts with sweat on the shirt, effort and getting back to some of the basic principles of what Everton Football Club has stood for for a long time.
"We want to bring back a good feeling. We need the fans, we need unity and we need everyone aligned. That starts with us as staff and players.
"Our aim is to put out a team that works, that fights and wears the badge with pride. The connection with the fans can then grow very quickly because they're so passionate.
"There is quality in this squad. But we have to make them shine. That's the job of me and my staff.
"We want to change the shape of this club going forward, remodel it in our style, but in a way that we can win.
"That's the task in front of us - make sure we're building, tactically and technically, giving players organisation, allow them the freedom to play, to go and enjoy their football because it's brilliant when the team's playing with a smile, but we've got to win."
Dyche's first game in charge of Everton will be against leaders Arsenal this weekend.
