The team exercised the options in the contracts for the 2009-10 season, meaning Morrison will make about $4.4 million in the final year of his rookie contract.
Dudley will make about $1.1 million in the 2009-10 season, the first of two option years the Bobcats hold for the 22nd pick in the 2007 draft.
Morrison was the third overall pick in the 2006 draft and is working his way back from major knee surgery that kept him out all last season.
Dudley averaged 5.8 points and 3.9 rebounds as a rookie last season.
The Bobcats signed power forward Justin Williams to a non-guaranteed contract, less than a week after he was waived by Golden State.
The 6-foot-10 Williams will get a tryout as the Bobcats look for depth in the frontcourt. The former Wyoming forward has averaged 3.4 points and 3.3 rebounds in 49 games over two seasons with Sacramento and Houston.