Davis was born in Sydney. He turned professional in 1974 and spent his regular career playing mainly on the PGA Tour of Australasia and the European Tour. He made the top ten of the European Tour Order of Merit four times in the late 1980s and early 1990s.
His seven European Tour wins included two of Europs's most prestigious tournaments, the British PGA Championship, which he won in 1986, and the season ending Volvo Masters, which he claimed in 1991.
His best finish on the PGA Tour was a tie for fifth at the 1986 NEC World Series of Golf. As a senior he has played mainly on the U.S. based Champions Tour, where he has one win, the 2003 Toshiba Senior Classic.
David represented Australia in team competitions several times, and was a member of his country's winning three man team at the 1986 Alfred Dunhill Cup.
1981 State Express Classic
1986 Whyte & Mackay PGA Championship
1988 Wang Four Stars National Pro-Celebrity
1990 Spanish Open, Wang Four Stars
1991 Volvo Masters
1993 Cannes Open
1977 McCallum's South Coast Open, Rosebud Invitational, Nedlands Masters
1978 South Australia Open, Nedlands Masters, West Australia Open, Mandursh Open
1979 Victoria Open
1985 Victoria PGA Championship
1986 Australian Open, Air New Zealand Open, New Zealand Open
1988 Bicentennial Classic
1989 Ford New South Wales Open
1990 Palm Meadows Cup
1991 SxL Sanctuary Cove Classic, AMP New Zealand Open
1992 SxL Sanctuary Cove Classic, Cookum Classic
1998 Mauritius Open
2003 Toshiba Senior Classic (Champions Tour)