The appointment of the former international showjumper was made by the new members council during its inaugural meeting last week.
David, 72, takes over from Lis Astall, who stepped down at the end of 2012 when her term came to an end.
Successes as a rider include three gold medals in the European Championships, two Olympic bronze medals and an individual gold medal in the World Championships.
He has won the King George V Gold Cup six times on six different horses — a record which still stands.
In 2010, David was made an ambassador for the sport.
This news story was first published in the current issue of H&H (17 January 2013)