Yates grew up in Charlotte, North Carolina, one of nine children. After graduating from Wake Forest High School and earning a mechanical engineering degree from Wilson Technical College in 1964, he joined the famed Holman-Moody organisation in 1968 as head of the air gauge department. Two years later he was hired by Junior Johnson to manage his team's engine department. From 1976 to 1986, Yates served as chief engine builder at DiGard Motorsports, during which time Bobby Allison won the NASCAR Winston Cup Series championship in 1983.
After a brief venture developing synthetic fuels, Yates returned to NASCAR in 1986 as general manager of Ranier-Lundy Racing. In 1988 he acquired the team outright, forming Robert Yates Racing with driver Davey Allison.
The team finished second in its very first race, the 1988 Daytona 500. Davey Allison won five races in 1991 and five more in 1992, the latter season including victory in the Daytona 500. The 1992 title fight went to the final race at Atlanta, where Allison needed a sixth-place finish to clinch, but a collision with Ernie Irvan damaged his car; Alan Kulwicki ultimately took the championship by a margin of ten points.
Tragedy struck in 1993 when Allison was killed in a helicopter crash in July. Ernie Irvan was recruited as his replacement and won at Martinsville and Charlotte before the season ended. In 1994 Irvan was critically injured in a practice crash at Michigan, ending his season.
With Irvan sidelined, Yates brought Dale Jarrett from Joe Gibbs Racing to drive the number 28 Ford. In 1996 Yates expanded to two full-time entries, pairing Irvan in the number 28 with Jarrett in the number 88. Jarrett won the 1996 Daytona 500 and the Brickyard 400 that year. The partnership with Jarrett culminated in the 1999 NASCAR Winston Cup Series championship, Yates's first title as an owner.
Elliott Sadler joined the team for 2003 and won two races in 2004. The team's final victory came with Dale Jarrett at Talladega Superspeedway in October 2005.
Yates retired from team ownership after the 2007 season, transferring the operation to his son Doug, who renamed it Yates Racing. In 2010, Yates came out of retirement to establish Robert Yates Racing Engines with his son-in-law Chris Davy.
Yates was diagnosed with liver cancer in late 2016. He died on 2 October 2017 at the age of 74. The following year he was inducted posthumously into the NASCAR Hall of Fame as part of the Class of 2018.
Robert Yates Racing won one NASCAR Winston Cup championship, two Daytona 500s, and a Brickyard 400 as team owner, while Yates's engines also powered championship-winning cars for other teams before he started his own outfit. His combination of mechanical genius and team-building ability made him one of the defining figures of the Winston Cup era, fielding cars for celebrated drivers including Davey Allison, Ernie Irvan, and Dale Jarrett across nearly two decades of competition.