The 33-year-old had been widely tipped for a move back to his home town to be closer to his family and a two-year contract was agreed after he passed a medical on Thursday, chief executive Alan Whiteley told the club's website.
"I am sure that Liverpool will agree that their loss is this football club's gain and the Craig's return will be met with huge excitement and enthusiasm by all Cardiff City fans - and as the perfect backdrop to the start of the new season," he said.
"I would also like to thank our manager for his tenacity and single mindedness in ensuring the transfer could take place - and for making my life a misery until such time as it could be completed.
"And of course to Brendan Rodgers and Liverpool Football Club; their assistance and support during the process of negotiations have been conducted in an extremely professional and amicable manner."
