Chhan was convicted in 2002 on two counts of misdemeanor domestic violence, and Pheach was convicted in 2005 of possessing drugs and obstructing a police officer.
"He wants to show mercy", Fox chief national correspondent Ed Henry said.
Brown has always been at odds with the Trump administration over immigration.
In early March, the Department of Justice filed a federal lawsuit against the state and its top officials to stop a cluster of so-called "sanctuary state" bills.
Sokha Chhan fled the Khmer Rouge in Cambodia at 13, then lived as a legal US resident for 35 years.
Alaniz, convicted in 1997, served five months in prison and 13 months on probation. The pardon statement said that Alaniz is active in his church and volunteers for a youth sports program. He is from Macau, which became part of China after his family moved to California when he was three.
Maher, for example, began working for the nonprofit Ecology Center in Berkeley after prison. All of the men had previously been convicted of felony crimes and faced deportation.
Mena was convicted in 2003 of possession of a controlled substance for sale and served three years of probation.
The pardons will not prevent the immigrants from being deported, according to ABC News, but could give their lawyers stronger cases to keep them in the United States. "It's a power given to governors and presidents because people think that you should be allowed to forgive people".
For ex-convict immigrants, deportation is a severe punishment that is often unwarranted, said Angelica Salas, executive director of the Coalition for Humane Immigrant Rights, which seeks to change California's laws to help immigrants avoid deportation.
Trump has been criticized for his own pardon, that of former Arizona Sheriff Joe Arpaio, who was convicted previous year of a misdemeanour contempt charge for flouting the courts in carrying out his signature immigration patrols.
This was the third time when Democrat Brown stood up on behalf of immigrants and pardoned them.
In a news release about the pardons on Friday, the governor's office said that "those granted pardons all completed their sentences years ago and the majority were convicted of drug-related or other non-violent crimes".
David Weigel and Matt Zapotosky contributed to this article.