George Argyros was born in Detroit, Michigan, and raised in Pasadena, California. Argyros is a second-generation American citizen; his grandparents emigrated from Greece. Argyros graduated from Chapman University in 1959 with a major in Business and Economics. He later served on the board of trustees of that university, including chairman of the board from 1976 to 2001. The Chapman University, Argyros School of Business and Economics is named in his honor.

In 1981, Argyros bought the Seattle Mariners. Argyros sold the team to Jeff Smulyan in 1989. Argyros had openly tried to purchase the San Diego Padres in 1987 and to sell the Mariners to local buyers, but a final deal was never consummated with Padres owner Joan Kroc.

Argyros served as a member of the Advisory Committee for Trade Policy and Negotiations for the U.S. Trade Ambassador. He resigned from that position in 1990, when President Bush appointed him to the board of the Federal Home Loan Mortgage Corporation (FreddieMac). He completed his term on the FreddieMac Board in March 1993.

In 2001 Argyros was appointed Ambassador to Spain and Andorra. He was sworn in on November 21, 2001. Many viewed the appointment as a political reward for his fund raising efforts for the Republican Party.

In October 2013, George and Julia Argyros announced two $1 million donations benefiting the arts in Julia's hometown of Adrian, Michigan. One was to help kick off a $3.5 million capital campaign for the Croswell Opera House and another was to benefit a fine arts education endowment through the Adrian Schools Educational Foundation.