A hearing has been scheduled for later this month and, if all goes as expected, Gibson will withdraw his plea, the case will be dismissed and his record will be expunged.
Gibson, 58, was charged with hitting his then-girlfriend in the mouth during a heated argument in 2010.
He made a plea agreement in 2011, and his attorney said he has since completed all the terms of the pact, including 16 hours of community service and 52 weeks of counseling.
Gibson was also placed on three years of probation, which ended in March 2014.
The Lethal Weapon and Braveheart star dated Grigorieva, a Russian musician and the mother of his 5-year-old daughter, after he and his wife, Robyn, separated following 26 years of marriage. The longtime couple and parents of seven children split up in 2006 when Gibson was arrested for drunken driving and made anti-Semitic remarks to a police officer. He later publicly apologized for his behavior.