Born in Fetsund, in the county of Akershus, Norway, Stenerud came to the United States as a college student, on a ski jumpingscholarship to Montana State University in Bozeman. In the fall of 1964, Stenerud was training for the upcoming ski season by running the stadium steps of Gatton Field, the football venue through 1971, directly south of Romney Gym. That day, he was cooling down from a workout by kicking a football with injured halfback Dale Jackson. Stenerud had played soccer as a youth in Norway, and his right leg's prowess was observed by basketball head coach Roger Craft, while he walked to the nearby Fieldhouse. Craft notified football head coach Jim Sweeney of the Norwegian ski jumper's kicking abilities, and Sweeney offered him a tryout, which was successful. Though ineligible for football competition that season, Sweeney encouraged Stenerud to suit up with the team for the final home game of 1964, to help him better understand the unfamiliar American game.
Following the ski season, Stenerud joined the football team for spring drills in 1965 and as a junior that fall he kicked a 59-yard field goal, then a college football record, in a 24–7 home win over rivalMontana. In 2013, Stenerud recalled that he had a significant tail-wind aiding him on that kick in Bozeman; the ensuing kick-off went over the end-zone bleachers at Gatton Field, whose elevation exceeded 4,900 feet (1,490 m) above sea level. He was named an All-American by The Sporting News as a senior in 1966, and was also an All-American in ski jumping and a three-time Big Sky champion.
Stenerud was one of the first professional football players to be used as a dedicated kicker, because of his excellent "sharpshooting" ball-kicking performance. He was one of the first placekickers to use the "soccer style", a technique the Hungarian-born Pete Gogolak had recently introduced in the AFL. During his first three years as professional, the last seasons for the AFL, Stenerud hit 70% of his field goals, compared with a 53% average for the other kickers in the AFL and NFL.
On Christmas Day1971, the Chiefs hosted the Miami Dolphins in an AFC divisional playoff game. In perhaps his toughest day as a pro, Stenerud made a 24-yard field goal in the first quarter, but then missed from 29 and 32 yards, the latter with 35 seconds remaining in regulation, and had a 42-yarder blocked three minutes into overtime. The Dolphins won 27–24 in double overtime on a 37-yard field goal by Garo Yepremian. Through 2013, the game remains the longest in NFL history at 82 minutes, 40 seconds of playing time, and was also the final football game in Municipal Stadium.
Stenerud retired after the 1985 season, his 19th (3 AFL, 16 NFL). He converted 373 out of 558 field goals (67 percent) and 580 out of 601 extra points (97%) for a total of 1,699 points scored. At the time of his retirement, he was the longest-tenured (19 years) professional football player to have played in the AFL. The last former AFL player was Charlie Joiner (Houston Oilers, 1969), who retired from the San Diego Chargers after the 1986 season.
In recent years, Stenerud has been involved in a Kansas City firm involved in designing stadiums and sports arenas. He also worked as a commentator for Scandinavian TV channel TV3's Super Bowl Sunday coverage in the 1990s, and still maintains strong ties with his native Norway. The street where he grew up, in the municipality Fetsund, was renamed in his honor.