Spanos was born in Stockton, California to a Greek family, the son of Greek immigrants, Constantino and Evanthia Spanos. His Father owned a bakery where the young Spanos started working at the age of eight. In 1942 he dropped out of college and joined the Army Air Force training as a pilot but left the program and instead served as a tail gunner during World War II. Spanos earned varsity letters in swimming and diving at the University of the Pacific in Stockton and later distinguished himself as an amateur Golfer.

In 1948, Spanos married Faye Papafaklis. They have four adult children: Dean Spanos, the Chargers' team president; Michael Spanos, the Chargers' executive vice president; Alexis Spanos Ruhl, a vice President of A.G. Spanos Companies; and Dea Spanos Berberian, a vice President of A.G. Spanos Companies. The Spanoses reside in Stockton, California. Spanos also owns property in Las Vegas, Nevada. Spanos had a seven-way heart bypass in 2000, and has had surgery and undergone chemotherapy for colon cancer. After his heart bypass at Sacramento Mercy General Hospital, Spanos donated $10 million to the hospital to sponsor the construction of its new state-of-the-art heart center.

In 1951 he borrowed $800 from a local banker to buy a truck which he then used to sell sandwiches to migrant farm workers in the San Joaquin Valley. By 1955 he had made his first million dollars. He invested his earnings in real estate and at the suggestion of his tax accountants, started to build apartments. In 1960, he founded A.G. Spanos Companies, which by 1977 had become the largest apartment builder in the United States. The corporation is based in Stockton and has 10 subsidiaries.

He has written a book called Sharing the Wealth: My Story which details his rise from a moneyless man of 27 years to become a Billionaire. Spanos was the first person ever to be on the winning teams in both the Bob Hope Desert Classic in Palm Desert (1977) and the Bob Hope British Pro-Am (1980). Spanos has suffered from severe dementia since 2008.

In 1984, Spanos bought 60% of the San Diego Chargers (now Los Angeles Chargers) from majority owner Eugene Klein for $48.3 million. Over the next 10 years, he bought out the shares of several small co-owners, bringing his control of the team to 97%. The remaining 3% was held by San Diego restaurateur George Pernicano, an investor in the team since a few years after its inception, until Pernicano's death in October 2016. Since 1993, Spanos' son Dean has handled the daily operations of the franchise. According to Forbes, as of 2015 the San Diego Chargers are worth $995 million.

Spanos was one of the largest contributors to George W. Bush's re-election campaign in 2004. By contributing $5 million to 527 groups that supported the Bush campaign in 2004, Spanos ranked among the top five GOP donors. President Bush appointed Spanos to the Kennedy Center board in 2004. Spanos was inducted into the California Building Industry Hall of Fame in 2005. Spanos also received the AHEPA Award, an award that recognizes members of the community for their contributions and achievements in their chosen field of endeavor.