After graduating from high school, Wirth attended the University of Colorado, where he earned a bachelor's degree in chemical engineering in 1982.^[3] Wirth played football and basketball at school.^[4]

Wirth joined Chevron as a design engineer^[5] in 1982. He worked in multiple sectors including engineering, construction, and operations.^[2]In 2001 he became president of marketing for Chevron's Asia, Africa and Middle East region.^[6]

He has been on the board of directors for Caltex Australia and GS Caltex.^[7] In 2018, Wirth was widely speculated and eventually confirmed to succeed John S. Watson as CEO of Chevron.^[1][2]

Wirth is a member of the board of the American Petroleum Institute, a trade group in the oil industry.^[8]

Wirth's company, Chevron, is responsible for one of the highest total carbon emissions of any private company worldwide.^[9] Despite these practices, Wirth's company has been involved in several greenwashing tactics, and was found by a Federal Trade Commission to be misleading its customers on its efforts to reduce greenhouse gas emissions.^[10] In response to CNBC host Jim Cramer asking if Chevron had considered calls to invest in alternative energy, Wirth responded that Chevron would "go back to our shareholders and let them plant trees".^[11]

In 2022, the Guardian newspaper named Wirth one of the US' top 'climate villains' due to Chevron's "greenwashing tactics to downplay the company’s environmental impact".^[9]

Wirth and his wife have four adult children.^[12]

Wirth sleeps less than 6 hours per night, waking at 3.45am to do a 90 minute gym session.^[13]