Wheaton stood at the side of Jeff Tarango in the doubles final of the junior tournament, the U.S. Open in 1986. In individual he lost there in the quarterfinals Javier Sánchez. The following year, he won the U.S. Open junior title by a final victory over Andrei Cherkasov. He studied one year at Stanford University and won the 1988 NCAA individual title. In the same year he became a professional tennis player and was able to win in January 1989, a first round at the ATP World Tour, when he reached through a victory over Luke Jensen the second round in Wellington. In August of that year he came in Stratton Mountain for the first time in a semi-final before, here he defeated one after Andre Agassi and Jim Courier before he was defeated in three sets Brad Gilbert. His first single tournament he won in 1990 in Kiawah Iceland, the same year he also won his first doubles title. In 1991 he won the Grand Slam Cup in Munich by a final against Michael Chang, Michael Stich after he previously had defeated in three sets, each of which was decided in the tie-break. Due to a hip injury in 1994, an Achilles tendon injury in 1996 and an elbow surgery in 1998, he could not build on its previous achievements later. His last semi-final on the ATP World Tour, he reached in July 1997 in Washington, after which he played mainly on the ATP Challenger Tour, where he partially had even there by the qualification. Throughout his professional career he won a total of three singles and three doubles titles. His best finish on the tennis world ranking he reached in 1991 with position 12 and position 24 in the single in a double.
His best individual result at a Grand Slam tournament was the semi-finals at Wimbledon in 1991, where he failed after beating Petr Korda, Cédric Pioline, Ivan Lendl Jan Gunnarsson and Andre Agassi in straight sets to Boris Becker. In the doubles competition, he stood with Paul Annacone in the finals of the U.S. Open in 1990 and with Patrick McEnroe in the final of the Australian Open in 1991. During reach him in an individual after 1991 no major success in Grand Slam tournaments more, he could double at the 1995 French Open and Open yet reached at the 1998 Australia each have a semi-final.
Wheaton graduated in 1993 two singles matches for the U.S. Davis Cup team. In the 1-4 defeat in the first round of the World Group against Australia he lost his first singles match against Mark Woodforde, the insignificant last singles match against Wally Masur he won in straight sets, and thus brought the single point for the United States. Previously, he had his country represented at the 1991 Hopman Cup, where he took on the side of Zina Garrison in mixed doubles.
In 2001 he retired from professional sports.