Donnelly attended Arizona State University and turned pro tennis in 1983. He wasn't particularly successful in singles, but in 1986 he made it into the top 50 of the tennis world rankings . This was due to his participation in the round of 16 at the US Open and the quarter-finals in Stockholm . However, these successes were the absolute exception in his career. Donnelly was much more successful in men's doubles. Between 1984 and 1989 he won eight double titles on the ATP World Tour and was in a double-final ten more times. He has played with various doubles partners over the course of his career, but his most frequent partners have been Peter Fleming and Mike DePalmer . In 1989, towards the end of his career, he played a few tournaments with Pete Sampras . He reached his highest world ranking in doubles in 1986 with position 16.
His best individual result in a Grand Slam tournament was reaching the round of 16 at the 1986 US Open. Surprisingly, Donnelly, known as a pure doubles specialist, beat the more highly rated Jakob Hlasek , Eliot Teltscher and Anders Järryd . He finally lost to Boris Becker in four sets . In the doubles competition he reached the double finals at Wimbledon in 1986 on the side of Peter Fleming. In addition, he was once in the semifinals of the French Open and the US Open. There he reached the quarterfinals in mixed 1985 .