Mueller started playing golf in 1962, at 14 years of age, at Lund Academic Golf Club, after his family had moved from Tranemo to Malmö. Five years later, he owned the course record at Lund AGC. As an amateur, Mueller won the Swedish National Junior Championship and represented Sweden both on junior level and in the European Amateur Team Championship. Still an amateur in 1970, he finished 35th in a professional tournament, the Dutch Open. He won one of the three major amateur tournaments at the time in Sweden, the 1971 Scandinavian International Match Play Championship, beating Henry Knudsen, Denmark in the final 4 and 3.
Professional career
Turning professional after the 1972 season, Mueller was one of the first Swedish born full-time touring professionals and played both on the Asian Golf Circuit and the European Tour. He was also first Swedish player to qualify for all four rounds in The Open Championship, an achievement reached in 1973, at Royal Troon Golf Club, Scotland. Mueller played 82 tournaments on the European Tour 1973–1981, with a best finish of tied 14th in the 1976 Italian Open. In 1976, he played 10 tournaments on the European Tour and made the cut in nine of them, to finish a career best 87th on the Order of Merit. Mueller represented Sweden twice in the World Cup and achieved some success. In 1975 in Bangkok, Thailand, his second round 68, was best in the field and in 1978 in Honolulu, Hawaii, he finished tied 5th in the individual competition and tied 14th in the team event. At the time, this was by far the best Swedish individual and team performances in the history of the World Cup. Mueller was awarded Swedish Golfer of the Year, male and female, in 1971 and won the Swedish PGA Championship four times. After his last of those victories in the fall of 1981, he retired from international competition and begun a career as a club pro, at Österlen Golf Club in southern Sweden, the following season. In 1991 he won the Swedish PGA Club Pro Championship. In 2019, Mueller, shooting his age of 71 in one round, won the club championship at Österlen Golf Club, 53 years after he won the same title for the first time, in 1966. First time Mueller scored his age over 18 holes, was at Viken Golf Club outside Helsingborg, Sweden, in 2009 when he was 61 years old. Being a Swedish and Scandinavian pioneer, during a time before, later coming, increase of prize money, his efforts to compete on the professional golf circuits is regarded as important inspiration for later generations of Swedish golfers and their successes around the world. In the book, celebrating the 75-year anniversary of the Swedish Golf Federation in 1979, he was, by the editor, pointed out as Sweden's best male golfer ever. At the opening of the Swedish Golf Museum in June 2000, he was one of ten players, among names as Annika Sörenstam and Jesper Parnevik, presented as important in the history of Swedish golf. In 1999 he received The Merit Sign in Gold by the Swedish PGA and was appointed Swedish PGA professional of the century by the magazine "Tournytt".
Amateur wins
1968 Swedish Junior Matchplay Championship, Lunds Vårtest
1969 Landskrona 36 holes, Rya Foursome
1970 Lunds Vårtest, Scandinavian Foursome
1971 Scandinavian International Matchplay Championship
Note: The Swedish Golf Tour was established in 1984 and the Nordic Golf League was established in 1999 consisting primarily of tournaments on the national tours of Denmark and Sweden.
Other wins (1)
1991 Swedish PGA Club Pro Championship
Team appearances
Amateur
European Youths' Team Championship : 1967, 1968, 1969