Born in Green River, Wyoming, Gowdy attended the University of Wyoming where he was a member of the Alpha Tau Omega fraternity . Gowdy made his broadcasting debut in 1944 in Cheyenne, Wyoming broadcasting a high school football game from atop a crate in sub-zero weather. His distinctive play-by-play style during his subsequent broadcasts of baseball and basketball in Oklahoma City earned him a chance with the New York Yankees and Mel Allen in 1949. In 1951, Gowdy became lead announcer for the Red Sox, and for the next 15 years, called the exploits of generally mediocre Red Sox teams on WHDH radio and on three Boston TV stations: WBZ-TV, WHDH-TV, and WNAC-TV. During that time, Gowdy partnered with two future baseball broadcasting legends: Bob Murphy and Ned Martin.

Gowdy's numerous network television assignments, first for ABC and later for NBC and CBS, covered a wide range of sports, earning him the nickname of the "broadcaster of everything." He was present for some of sports' storied moments, including Ted Williams' home run in his final at-bat in 1960, Franco Harris' "Immaculate Reception", and Hank Aaron's 715th home run. In an interview done by NFL Films, Gowdy said his most memorable game was Super Bowl III when the New York Jets defeated the Baltimore Colts after Joe Namath guaranteed victory. He was also known for the occasional malapropism, including a consoling comment just after the Red Sox lost the 1975 World Series: "Their future is ahead of them!"

Over the course of a career that stretched into the 1980s, Gowdy covered the American Football League and National Football League, Major League Baseball, college football, and college basketball. He was involved in the broadcast of 13 World Series, 16 baseball All-Star Games, nine Super Bowls, 14 Rose Bowls, eight Olympic Games and 24 NCAA Final Fours. He also hosted ABC's long-running American Sportsman series.

In 1970 Gowdy became the first sportscaster to receive the George Foster Peabody Award. He was elected to the National Sportswriters and Sportscasters Hall of Fame in 1981. In addition, he was given the Ford C. Frick Award from the Baseball Hall of Fame in 1984, the Pete Rozelle Award from the Pro Football Hall of Fame in 1993 and a lifetime achievement Emmy in 1992, and was selected to the Boston Red Sox Hall of Fame in 1995. Gowdy was president of the Basketball Hall of Fame for several years, and that institution's Curt Gowdy Award, presented annually to outstanding basketball writers and broadcasters, is named after him; he was one of its first two recipients.

In 1963, Gowdy purchased radio stations WCCM and WCCM-FM in Lawrence, Massachusetts, later changing the FM station's call letters to WCGY to somewhat match his name. Gowdy also owned several radio stations in Wyoming, including KOWB and KCGY-FM in Laramie. He sold his broadcast interests in Massachusetts in 1994 and his Wyoming stations in 2002.

Gowdy was said to have a warm, slightly gravelly voice and unforced, easy style that set him apart from his peers. Unlike many well-known announcers, Gowdy never developed catch-phrases or signature calls, but merely described the action in a straightforward manner. Example:

"The ball's hit deep... deep... it is gone! He did it! He did it! Henry Aaron... is the all-time home run... leader now!" He came out of retirement in 2003 to call a Red Sox game at Fenway Park as part of ESPN's Living Legends series.

Gowdy died at age 86 in Palm Beach, Florida from leukemia.