Anderson died of pneumonia at Ronald Reagan UCLA Medical Center, a family spokesperson said.
The Century City-headquartered holding company owns 33 subsidiaries involved in insurance, real estate, financial services, wholesale beverage distribution, automobile dealerships and manufacturing.
A lawyer who co-founded the Los Angeles law firm of Kindel & Anderson in 1953, Anderson launched his business empire in 1956 with the purchase of a Hamm's beer distributorship in downtown L.A.
"We began modestly, carefully and prudently, and moved as the opportunities came," he told The Times in 1987, the year he and his wife, Marion, donated $15 million to the UCLA Graduate School of Management.
The donation was described at the time as being the largest gift by an individual ever received by the University of California and the third-biggest given to a U.S. graduate school of business.
In recognition of the gift, which was the cornerstone of a fundraising campaign to build a $50-million facility for the graduate business school, it is now known as the UCLA Anderson School of Management.
In 1995, he received both the UCLA Alumnus of the Year Award and the UCLA Medal.
In April, the UCLA Anderson School of Management announced a $25-million gift from the Andersons, the largest in the school's history. That brought the amount the couple had donated to the school to nearly $42 million.
"UCLA is very important to me," Anderson, a 1940 graduate, told The Times in 1987. "It got me started on the right path."
The son of a barber, Anderson was born Sept. 12, 1917, in Minneapolis, where he sold popcorn in front of his father's shop as a boy. The valedictorian of his high school class, Anderson arrived in Los Angeles in 1936 with a hockey scholarship to UCLA.
While earning a bachelor's degree in business administration, he spent his early morning hours keeping the books for a local builder and spent his weekends working at an open metal heat-treating oven at North American Aviation.
After graduating from UCLA in 1940, Anderson earned an MBA from the Harvard Graduate School of Business in 1942. He passed his CPA exam while serving on the staff of a Navy admiral during World War II.
Back in Los Angeles after the war, he worked at the Arthur Andersen & Co. accounting firm during the day and attended Loyala University School of Law at night.
In 1953, three years after earning his law degree, he and James H. Kindel Jr. founded the Los Angeles law firm of Kindel & Anderson.
Anderson was presented with his first business opportunity in 1956 when the Hamm's Brewing Co. asked for his help in finding a buyer for the company's struggling distributor in downtown Los Angeles.
As chronicled in Forbes magazine in 1988, the year he first appeared on the Forbes list, Anderson already had represented more than 15 area beverage distributors as a lawyer. He knew the business.
With a reported $60,000 loan guaranteed by a friend, he took over the distributorship himself.