Davis, 72, has won four recommendations for release from the California parole board as of the board's decision Thursday. Three earlier decisions for his release were later reversed by California governors.
Brown reversed the 2012 and 2014 decisions, and then-Gov. Arnold Schwarzenegger reversed a 2010 recommendation.
The parole board's decision is not the end of the case. There's a 120-day internal review period after which the decision can be affirmed or reversed. When that's done, Brown will have 30 days to decide whether to nullify or modify the decision.
Evan Westrup, a spokesman for Brown, said the governor wouldn't comment before the reviews.
According to a statement from the California Department of Corrections and Rehabilitation, Brown previously denied Davis' parole because he has withheld "information about the murders of Gary Hinman and Donald Shea, and minimized the extent of his involvement and leadership within the Manson family."
CNN left a message seeking comment with Davis' attorney, Michael Beckman, but didn't immediately hear back.
California has initiated a program for the early release of elderly and frail prisoners to help comply with a court order to relieve prison overcrowding.
A representative for the Hinman family condemned this week's decision to grant parole to Davis.
"I have attended four of the last parole hearings for Mr. Bruce Davis, none of them quite like this one," Debra Tate said.
"I have taken over 11 pages of notes where the commissioners asked Mr. Davis to explain himself on multiple unsavory actions that he has taken in the past, including making a weapon from a kitchen spoon," Tate said.
"One would think that all of these actions would be followed by a denial of parole for this individual. However, under Gov. Brown's newly implemented 'elderly inmate act,' the commissioners have no choice but to release this very dangerous inmate into a free society," she said.
"It is my sincere hope that everybody will pick up and send an email to let Gov. Brown know what kind of legacy he will be leaving if he were to unleash criminals such as serial killers and gang members back into a free society," Tate said.
Tate's sister Sharon was also killed by Manson followers.
Davis was sent to state prison on April 21, 1972, for the first-degree murders of Hinman, a musician, and Shea, a stuntman, in 1969.
In 2010, 2012 and 2014, the parole board granted Davis parole.
In the second case, the board explained it made such a recommendation because of Davis' "positive adjustment, record of no recent disciplinary problems, and for successfully completing academic and vocational education and self-help programs."
If Davis is successful this time, he would become the first Manson "family" member to be freed solely for good behavior.
The Manson group's gruesome killings inspired the best-selling book "Helter Skelter" and made their ringleader Manson a cult figure.
The two-day rampage in 1969 killed seven people, including 8-months-pregnant actress Sharon Tate, wife of famed movie director Roman Polanski.
Manson, 80, is serving a life sentence for his role in the seven murders and those of Hinman and Shea. He was denied parole for the 12th time in 2012
. His next hearing is set for 2027.