Prison officials said both deaths are being investigated as suicides.
Urdiales, a former marine, was sentenced in October for the murders of five women in San Diego, Mission Viejo, Palm Springs and Cathedral City during the 80s.
He had been previously sentenced to death in Chicago and Livingston County, Illinois, in two separate trials for committing three murders, but when the death penalty was abolished in Illinois he was re-sentenced to life without parole.
He was then brought to Orange County in 2011 to be tried for the five murders in Southern California.
He was formally sentenced to death on October 5.
The other death row inmate found dead on Sunday night at San Quentin, Viendra Govin, was convicted for the murders of four people.
A Los Angeles County jury sentenced Govin to death in 2004.
His brother, Pravin Govin, has been on death row since 2005 for taking part in the crimes as well.
Both brothers were convicted for strangling, beating and burning four members of a family who owned a motel next to their own in Studio City.
A business dispute led to the Govin brothers killing Gita Kumar, 42, Plara Kumar, 18, Tulsi Kumar, 16, and Sitaben Pate, 63, in their home and then setting the home on fire.
A business partner, Carlos Amador pleaded guilty and was sentenced to prison.
Prison officials do not believe Govin and Urdiales’ deaths were related.
California has not executed anyone since 2006 and inmates are more likely to die from suicide or old age.
According to figures, since 1978, when California reinstated the death penalty, 79 condemned inmates have died from natural causes, 25 have committed suicide, 13 have been executed in California.
Only one was executed in Missouri and one was executed in Virginia.
There currently are 740 offenders on California’s death row.