Bamba, 30, has agreed a two-year deal with the option of a further year to end speculation over his future.
He becomes Leeds' third summer signing following the recent arrivals of striker Lee Erwin and goalkeeper Charlie Horton.
Bamba joined Leeds on loan from Palermo in January and became a permanent feature at the heart of defence, making 19 appearances and being named skipper on several occasions.
Before joining Palermo last summer the former Leicester centre-half spent two seasons in Turkey with Trabzonspor.
He has also had spells at Dunfermline and Hibernian after starting out in France with Paris St Germain.
Bamba's future at Leeds had been in doubt after he publicly critcised the way the club was being run at the end of last season.
The Ivory Coast international had only signed a three-year deal when he joined Palermo last August.