Oosting was trained at the Dutch Tennis Training Institute, where Jacco Eltingh also trained. In 1983 he became a professional tennis player and was the national Dutch tennis champion in 1987 and 1988. He stood in 1990 in the semifinals of the Challenger tournament in Bangkok and in the quarterfinals of the Challenger tournament in Kuala Lumpur .
In 1991 he reached a double-final on the ATP World Tour for the first time . The following year he won his first double title in Munich alongside David Adams . With changing partners he won seven double titles in the course of his career, and he made it into a final eleven times. He reached his highest ranking in the tennis world rankings in 1988 with position 72 in singles and 1995 with position 20 in doubles.
His best individual result in a Grand Slam tournament was reaching the round of 16 at the Australian Open in 1988. His best result in the doubles competition was participation in the quarter-finals at the Australian Open in 1991. At the French Open , Wimbledon and the US Open , he was in Round of 16. He was even more successful in mixed . He won the 1994 French Open alongside Kristie Boogert .
Oosting played eight singles and three doubles games for the Dutch Davis Cup team between 1985 and 1988 . However, he was never used in the world group and played in games against Finland , Nigeria , Israel and Senegal .