Robert Irsay became owner of the Colts on July 26, 1972, when he traded his recently-acquired Los Angeles Rams to Carroll Rosenbloom for the Colt franchise. Irsay had purchased the Rams from the estate of former owner Dan Reeves.

Irsay was born on March 5, 1923, in Chicago, Illinois. He worked his way through the University of Illinois, where he earned a Bachelor of Science degree in mechanical engineering. While attending the University of Illinois, Irsay was an Illini football teammate of future Colt Alex Agase.

From 1941 to 1945, Irsay served in the United States Marine Corps, after which he worked for a mechanical contracting company in Chicago.

In 1952, he formed the Robert Irsay Company of Skokie, Illinois. After building the business into one of the largest and most respected heating, ventilation, and air conditioning companies in the world, Irsay sold his company to a firm listed on the New York Stock Exchange in 1971. He remained associated with the firm until 1978 when he formed Colt Construction and Development Co,., and its affiliate, Colt Developers Co., which were diversified construction and development companies.

Irsay remarked in 1984 upon moving the team to Indianapolis, "The greatest thrill I've had in football was on April 2, 1984, when I walked into the Hoosier Dome with Mayor (Bill) Hudnut in front of all those fans. It is my intention for the Colts to be a vital contributing member of the greater Indianapolis community."

Under Irsay's ownership, the Colts reached the playoffs six times and claimed four division titles.

Robert Irsay was an active philanthropist throughout his life, supporting several national and local charitable organizations. He owned the Colts until his death on January 14, 1997, when his son, Jim Irsay, assumed ownership of the franchise.