The Order of Merit is presented to a select group of individuals who have made significant contributions to the arts, science, education and public service.
Hockney, who was born in Bradford, England, is best known for his modernistic landscapes and still lives of swimming pools, living rooms and other "private spaces," the BBC said Sunday.
Howard was prime minister of Australia from 1996-2007. He oversaw Australia's involvement in the Iraq war and addressed major domestic issues such as gun control and Aboriginal rights.
The BBC said the Order of Merit was created in 1902 by King Edward VII. It is restricted to two dozen members as well as a small number of foreign recipients.