The centre-half joins for an undisclosed fee after agreeing a three-year deal with the option of a further 12 months.
Miquel made his first-team debut for Arsenal as an 18-year-old, but the Spaniard has not featured since February last year and was sent on loan to Leicester last season.
He said: "It's brilliant for me to come here, and I want to try and get in the team as soon as I can to help Norwich get back to the Premier League.
"I had to move on from Arsenal and Norwich have given me the chance to prove myself. The Championship is a tough league, but I know what it's about and I enjoyed it last season. I'm really looking forward to getting started."
Norwich boss Neil Adams said: "He's a defender who we know can play having come through the Arsenal system, and he had important experience with Leicester last year in the Championship. He's certainly one who can come in and give us strength on the left side of our defence."
Another player leaving Arsenal is Ryo Miyaichi, who has joined Dutch club Twente on a season-long loan.