The media are reporting a fee of approx £1m has been paid for the central defender with a further £250,000 due if we make the Premier league.
"I'm excited and pleased to have completed the move," Hudson told the club's official website.
"I met the manager and the chairman and they showed me around the new stadium and the training ground and it looked superb.
"I'm looking forward to linking up with the lads now and getting started. Cardiff went pretty close last year and hopefully this time around we can take that one step extra.
"Cardiff is a great club and whenever I have played here the supporters have always been superb for the home team and I'm looking forward to running out at the new stadium with a full house - the atmosphere I'm sure will be fantastic."