The 35-year-old had long spells with Sunderland, Everton and Wigan before moving to Hull where his contract expired at the end of last season.
Kilbane, who can operate anywhere down the left flank, has signed a one-year contract at the Ricoh Arena.
Sky Blues boss Andy Thorn told the club's website: "This is another great signing for us. You only have to look at the clubs Kevin has played for and his record at international level to know his quality.
"He brings bags of experience to our squad and he will complement the younger players we have here and will help bring them on.
"Not only will he be an asset on the pitch, he will be a big player in the dressing room too so I am really pleased that we have acted quickly to bring him in."