Born in Hwaseong in the South Korean province of Gyeonggi, Cha Bum-kun began his football career with the South Korean Air Force club in 1971, the same year he became a Korean U-19 international. By 1972 he had been capped by the Korean national team as the youngest player in history called up to the squad. After developing into the top player in his country, Cha wanted to play in Germany's Bundesliga. Cha promised to learn skills in Germany and help Korea advance in football. He eventually rose to international stardom and fulfilled his promise by coming back to South Korea after his retirement and starting youth football clinics. He coached the national team in the 1998 FIFA World Cup and also Ulsan Hyundai and Suwon Samsung Bluewings of the K-League.
Cha started his career in the Bundesliga at age 25. In December 1978, he was transferred to SV Darmstadt, where he spent less than a year before being snapped up by Eintracht Frankfurt. Cha made an immediate impact with his new club, scoring in three consecutive games. Frankfurt went on to win the UEFA Cup in the 1979–80 season. He was widely considered one of the best forwards in the Bundesliga throughout his career. He became the third-highest-paid footballer in Germany. In the 1981 season, in a game against Leverkusen, he suffered a near career-ending knee injury.
In 1983 he was transferred to Bayer Leverkusen. He won a second UEFA Cup with them in 1988. Cha scored a dramatic equalizer against Espanyol to tie the game 3–3. Leverkusen eventually went on to win the game on penalties.
Cha retired in 1989 after a long Bundesliga career spanning 308 games in which he scored 98 goals (none from penalty kicks), then the highest for a foreign player in the league. Over his 10-year career, he received only one yellow card.
Cha was part of the South Korean national team of the 1986 FIFA World Cup finals, in Mexico, where they lost to Argentina and Italy but earned a draw against Bulgaria. The opposing teams were fully aware of Cha's scoring abilities and frustrated him by marking him with two defenders at all times. He did not score any goals in the tournament. Looking back, he recalled: "We didn't achieve our first win but the campaign was not disappointing as we played hard and well against the best teams in the world, including the eventual champions Argentina."
Cha moved into management with K-League side Ulsan Hyundai Horang-i, coaching them from 1991–1994. His next appointment in January 1997 was Korean national team coach and he led the nation to the 1998 FIFA World Cup; however, a disastrous 5–0 defeat at the hands of The Netherlands in Korea's second group game got Cha fired. He later blamed the Korea Football Association for the bad performance, citing lack of bonuses and alleging pro soccer games in Korea were fixed. The KFA promptly slapped a five-year ban on him and he soon left the country with his wife.
Cha is a devout Christian and list the three most important things in his life as 'family, religion and football'. Bum-Kun's second child, Cha Du-ri, is following in his father's footsteps. The younger Cha played in Germany and was converted from forward to defender, and now plays for FC Seoul after having his contract terminated with Fortuna Dusseldorf.
Cha's record of 17 league goals in the 1985–86 season remains as the highest goal-tally achieved by an Asian player in Bundesliga history. The finest effort to date in attempt to match Cha's feat was delivered by Iranian striker Vahid Hashemian, who scored 16 goals during the 2003–04 season with Bochum.
Cha is South Korea's all-time leading scorer with 55 goals in international A matches.