It follows the arrival of Josh Murphy from Norwich earlier this week as the Bluebirds prepare for life back in the Premier League after sealing promotion from the Championship.
Cunningham, who emerged from the youth setup at Manchester City and played five times for the first team, has signed a three-year contract that will keep him in Cardiff until June 2021.
“It’s fair to say that I’ve been an admirer of Greg for a number of years and that he’s consistently been one of the best left-sided defenders for club and country,” manager Neil Warnock told the club’s official website.
“We’re delighted to have his experience and knowledge so as to supplement Joe Bennett who had a great time last season.
“I anticipate that Greg coming in will give us a lot of strength down that left-hand side.”