The Spaniard, 32, has penned a one-year deal with the option to extend his stay by a further 12 months.
Cuellar had been without a club after leaving Sunderland at the end of last season.
"I'm so happy and so proud to join Norwich City. They've given me the opportunity to come here and I want to pay them back with performances on the pitch," he told the club's official website.
"It is a big club but it is looking to get bigger and stronger and to move forward. I see the same mentality that I have of trying to improve all the time, so I think we'll go hand in hand."
Cuellar's career in British football has included spells with Rangers, Aston Villa and Sunderland.