Douglas, 31, pleaded guilty in January to conspiring to distribute drugs.
In addition to the prison time, TMZ said he also was ordered to pay $25,000 in fines.
He is required as well to serve 450 hours of community service and spend an additional five years in a supervised release program once he completes his prison term, the entertainment news Web site said.
Michael Douglas' film credits include "Romancing the Stone," "Wall Street," "The Game" and "Wonder Boys."
Cameron Douglas appeared in the movie "It Runs in the Family," alongside his father Michael and grandfather Kirk.
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