Cardiff boss Neil Warnock has said he did not consider Wigan to be a "threat" once they appointed manager Warren Joyce in November.
Warburton, 54, has signed a two-and-a-half-year contract and will be joined at the City Ground by assistant David Weir.
Derby County have confirmed the appointment of Gary Rowett as their new manager.
Nottingham Forest are in talks with former Rangers and Brentford boss Mark Warburton, according to multiple reports.
Sheffield Wednesday head coach Carlos Carvalhal has been charged by the Football Association with improper conduct after being sent to the stands.