A district government in the eastern city of Wuxi said in an online statement that investigators concluded that the director of "Hero" and "House of Flying Daggers" and his wife, Chen Ting, flouted family planning policies by having the children without approval and before they were married.
China limits most urban couples to one child and rural families to two if the first-born is a girl.
The fines are based in part on the couple's annual income. The government of Wuxi's Binhu district said they made a total of about $580,000 in the years before each of the children were born.
News that Zhang had violated the country's one-child rule surfaced in March. Binhu authorities said in July that they were in charge of the investigation because Chen is a registered resident of the district even though she usually resides in Beijing.
By late last year, Wuxi family planning officials publicly complained they could not get in touch with Zhang, who eventually issued an apology for the "negative social impact" he had created and promised cooperation with investigators.
The case raised questions among members of the public about whether Zhang's social status had allowed him to dodge the family planning rules for years.
Zhang and Chen have 30 days to pay the fine. They may also seek an administrative review or file a court petition.