The two have been locked in a bitter dispute over custody and finances for over a year.
Los Angeles County Superior Court officials said a deal has been reached after several days of negotiations, but the details are not being made public.
Final terms will be worked out behind closed doors in the coming week.
Gibson was charged with misdemeanor domestic battery after a fight with Grigorieva in 2010.
He pleaded no contest in the case but admitted no guilt. The actor was ordered to undergo counseling and recently completed his community service by volunteering with a children's charity in Guatemala.
The case swept the Internet after recordings of racist and sexist rants by Gibson were leaked to the celebrity website RadarOnline.com. Sheriff's officials took possession of the recordings as part of their criminal investigation, but Grigorieva's attorney announced in May that he would no longer seek to use them against the former Hollywood superstar in the custody case.
The coming days could prove crucial for Gibson to resolve some of the messiness of his personal life in recent years.
Gibson, 55, recently reached a divorce settlement with his estranged wife, Robyn, and his attorney announced in June that the case should be finalized by Tuesday.
Robyn Gibson filed to end her nearly 28 year marriage in April 2009, just months before Grigorieva gave birth.
In recent months, both have appeared multiple times in court for hearings and meetings, but Gibson has not spoken publicly about the case.
The leaked conversations recorded by Grigorieva were the latest scandal for Gibson, who was arrested in 2006 for drunken driving; a deputy's report revealed he made a series of anti-Semitic and sexist slurs while in custody.
The Associated Press contributed to this report.
