Officers responding around 11:30 a.m. Wednesday to reports of a medical emergency found the 47-year-old Giambi dead at the residence, said Lt. Robert Ewing of the Claremont Police Department.
TAKE ACTION: Suicide Prevention - Local resources for those in crisis
The Los Angeles County Coroner's Office determined the cause of death to be suicide after Giambi suffered a gunshot wound to the chest.
Giambi's agent, Joel Wolfe, said the family requested "that we all respect their privacy during this difficult time."
RELATED: Former Oakland Athletics player Jeremy Giambi dies at 47, team says
A brother of five-time All-Star Jason Giambi, Jeremy Giambi spent six seasons in the major leagues as an outfielder and first baseman with Kansas City (1998-99), Oakland (2000-02), Philadelphia (2002) and Boston (2002-03).
Jeremy hit .263 with 52 homers and 209 RBIs. His best season was 2001, when he batted .283 with 12 homers and 57 RBIs for the Athletics.
TAKE ACTION: Get help with mental health issues
If you are struggling with thoughts of suicide, or worried about a friend or loved one, help is available. Call the National Suicide Prevention Lifeline at 1-800-273-8255 (TALK), or text TALK to 741-741 for free confidential emotional support 24 hours a day 7 days a week.
The Associated Press contributed to this report.