The conviction itself will remain on Downey Jr`s record.
In 1996, police found cocaine, heroin and a pistol in the actor`s car when they stopped him for speeding.
Downey Jr, who is best known today for his role as Iron Man in a series of Marvel films, was sent to prison in 1999 after violating his probation.
He had achieved early success in Hollywood after making his screen debut at the age of five, but went on to fall victim to drink and drugs, before spending time in rehab and rekindling his commercial success.
A proclamation from Mr Brown`s office says Downey Jr has "lived an honest and upright life, exhibited good moral character, and conducted himself as a law-abiding citizen".
It went on to say he "has paid his debt to society and earned a full and unconditional pardon".
Mr Brown has issued hundreds of pardons in each of his four terms in office, usually doing it around Christian holidays.
Most people pardoned along with Downey Jr had been found guilty of nonviolent drug and property crimes.
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