Garza is the son of a gasoline station owner and the grandson of Mexican immigrants to the United States. Garza received his Bachelor of Business Administration from the University of Texas at Austin in 1980 and received his Doctor of Jurisprudence in 1983 from Southern Methodist University School of Law.
After practicing as an attorney, Garza became a judge in Cameron County in 1988. He served as the Texas Secretary of State from January 1995 to November 1997 before later being elected as one of the three member board of the Texas Railroad Commission, where he served as chairman.
In 2002, he was appointed U.S. Ambassador to Mexico, a position he held until 2009. In 2009, the year he retired from the office, Garza received the Águila Azteca from Mexico in recognition of his work to strengthen the bonds between Mexico and the United States. This is the highest award that Mexico bestows on foreigners. Thereafter, he took a position as counsel with White & Case LLP and also as chairman of management consultancy firm Vianovo Ventures.
Garza married María Asunción Aramburuzabala, the President of Tresalia Capital who had a personal fortune valued at $1.8 billion, according to one source. The couple divorced in May 2010. He subsequently married Dr Liz Beightler.
