The 30-year-old, who has previously played for Leyton Orient, Exeter City, Peterborough United and Crawley Town, arrives at Carrow Road following a two-year stint at Portsmouth.
Jones, who has penned a two-year contract with Norwich, made 17 appearances for Pompey last season and also spent a 28-day loan at Crawley.
"It's one which has come a bit out of the blue but I'm really excited to get going now," Jones told Norwich's official website. "I've met all the lads and it's nice to have things done. I'm looking forward to getting settled into the club now.
"I had a season in the Championship with Peterborough a few years ago, so it's not a league that's foreign to me. I'm hoping to add experience to the squad."
"It was important we brought in someone with good pedigree in the Football League who could add to what we have. In Paul, we have a player who matches the qualities we are looking for well."