While Basham makes the move to the Arms Park, Cardiff and Wales flanker Thomas Young has been linked with a move to Rodney Parade.
Basham becomes the second new signing announced for next season, following fellow Wales international Ioan Lloyd in moving to the Welsh capital.
"I'm delighted to be joining Cardiff Rugby, it was time for me to take on a fresh challenge," said Basham.
"I really believe being part of the exciting group of players and coaches at the Arms Park will allow me to continue to develop as a player.
"Hopefully I can also add a different dimension and option to compliment the quality players already in the squad. I really can't wait to get started."
Cardiff have not specified the duration of Basham's contract.
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