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Everton did not say how much they had paid for the 29-year-old England international, who joined City from Aston Villa in 2015.
Delph played 89 games for City, winning two Premier League medals. He also has 20 England caps.
"When I look to bring a new player into our squad, the first thing I look for above all the other things is quality and Fabian is a player with high quality," Everton manager Marco Silva told the club web site.
"But what they can bring to our dressing room is also important."
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The web site also quoted Delph.
"Every time I have played against Everton, whether it was home or away, straight away the first thing that comes to mind when you see the fans is passion," he said.
"You are always going to hear Evertonians and I'm excited to play at home and hear them when I am playing."
"Hopefully we can push together, fans and players, to do something special."