Convicted Double Murderer Betty Broderick Dead at 78

Betty Broderick, the woman who shot and killed her ex-husband and his new wife in cold blood, has died ... TMZ has learned.

The California Department of Corrections and Rehabilitation tells TMZ ... Betty was pronounced dead Friday morning.

We're told Betty had been transported from the California Institution for Women prison to an outside medical facility back in April ... and she died in the facility.

CDCR says the doctor who pronounced her dead determined she died from natural causes ... though the San Bernardino County Coroner will determine her official cause of death.

Betty was serving a 32-year-to-life sentence for murdering Dan and Linda Broderick.

When Betty was married to Dan back in 1983, she confronted him ... accusing him of having an affair with Linda, his 21-year-old assistant. Dan denied it for 2 full years, but ultimately moved out of the house and confessed to the affair.

The divorce was brutal ... mostly over a custody war. Dan ended up getting full custody of their 4 kids.

In 1989, 7 months after Dan and Linda married, Betty stole a key from her daughter that opened the front door to Dan and Linda's house, and then shot and killed the 2 of them.

Betty was sentenced to 2 consecutive, 15-year-to-life terms. She was also convicted of illegal use of a firearm.

Betty was denied parole 3 times. She was eligible again in 2032.