The 29-year-old, who made 158 appearances for the Bluebirds during his five years at the club, joins the Trotters on a two-year deal.
Noone was expected to link up with Bolton on an initial half-season loan, but an agreement has instead been struck for the Championship club - who have to follow strict EFL transfer rules due to financial problems - to bring him in permanently for an undisclosed fee.
Speaking to his new side's official website, the former Brighton & Hove Albion midfielder said: "I am delighted to get it all sorted and I cannot wait to play for Bolton Wanderers.
"There had been some interest from other clubs, but Bolton was always my first choice. They are a massive club and I am looking forward to getting going."
Noone had fallen out of favour under Neil Warnock in South Wales, last featuring for Cardiff in the 2-0 defeat to Newcastle United in April.