Hughes joins Australian goalkeeper Michael Theklitos, defender Michael Nelson, midfielders Matt Gill and Owain Tudur Jones who have all arrived at the club this summer.
"We're delighted Stephen has chosen to join Norwich City, he had a number of options open to him and rightly spoke to his family and friends before making the decision," Gunn told the club's official website. "We faced stiff competition from clubs in the Championship, Scottish Premier League and also in the Bundesliga.
"I met with Stephen when we were up in St Andrews last week and had dinner with him. I told him our plans and how we see him fitting into them.
"He knows the set-up we've got at Carrow Road from playing here with Leicester City. Once again the lure of playing in front of a full house at Carrow Road has been a big factor in us landing a player and we need to thank our fans for that."