According to 'Sky Sports', Cardiff have agreed on an approximate fee of £3.5million for the defender, and Cunningham is set to remain at the Cardiff City Stadium until 2021.
The Republic of Ireland international is the the Bluesbirds' second signing of the summer transfer window so far, joining former Norwich forward Josh Murphy as Cardiff take on the Premier League.
Manager Neil Warnock told the club website: ''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.''
He added: ''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.''