Edwards was BYU's head football coach from 1972 to 2000. He had previously served as an assistant coach from 1962 to 1971. His offensive scheme was passing-dominated. He started coaching in an era when college football offenses were dominated by strong running attacks. His quarterbacks threw over 11,000 passes for more than 100,000 yards and 635 touchdowns. He got the idea to switch to a pass oriented team by looking at BYU's history. The BYU football program had struggled before Edwards with the notable exception of one conference championship that resulted from the aerial attack of Virgil Carter. This past success encouraged Edwards to open up the BYU offense. Edwards coached prominent quarterbacks such as Steve Young, Jim McMahon, Ty Detmer, Marc Wilson, Robbie Bosco, Gary Scheide, Gifford Nielsen and Steve Sarkisian. at Brigham Young University Awards won by his players include a Heisman Trophy, a Doak Walker Award, a Maxwell Award, two Outland Trophies, four Davey O'Brien Awards, seven Sammy Baugh Awards, 34 All-America citations, 11 conference player of the year and 24 Academic All-America player citations. In 1984, he was named National Coach of the Year after BYU finished the season 13–0 and won the National Championship. Edwards retired after the 2000 season with a 257–101–3 record. Prior to Edwards' final game, BYU renamed its home field, Cougar Stadium, as LaVell Edwards Stadium in his honor. The stadium had almost doubled in his capacity during his tenure, from 35,000 people when he took over the program to over 65,000 people upon his retirement. At the time of his retirement, he ranked sixth all-time in victories, and second all-time in victories with a single program. Edwards received the Amos Alonzo Stagg Award, presented by the American Football Coaches Association, in 2003. In the 1980 Holiday Bowl, BYU rallied from a 45–25 deficit with only 4 minutes to play to defeat Southern Methodist University. Following the 1984 national championship, Edwards was offered the head coaching positions with the Detroit Lions as well as the University of Texas at Austin, but he turned down the offer.
While head football coach at BYU, Edwards also earned a doctorate. Following his retirement from coaching, Edwards remained a prominent leader and speaker for members of the LDS Church, which owns and operates BYU. He and his wife served an 18-month mission for The Church of Jesus Christ of Latter-day Saints in New York City during 2002–2003.
Death
Edwards suffered a broken hip on December 24, 2016 and died five days later at his home in Provo on December 29, at the age of 86. A public memorial service was held at the Utah Valley Convention Center in Provo on January 6, 2017. A private funeral service for family and friends was then held the next day, on January 7.