He was a rear admiral in the U.S. Public Health Service Commissioned Corps, and served as the Deputy Surgeon General of the United States under President Carter from 1978 to 1981.

[1][2][3][4][5][6] Greene was known for his Oral Hygiene Index (with coauthor Jack Vermillion; Greene Vermillion 1960), which provided a systematic approach to quantifying bacterial plaque on teeth, his role in creating public policy for treating dental patients during the AIDS outbreak in the 1980s, and his work to prevent smokeless tobacco use among professional baseball players (Ernster et al.

[1] His work took him around the world studying the health impact of the environment on indigenous people in South America, India, and Asia.

[1] He authored more than 100 publications[12] and is known for his Oral Hygiene Index,[13] which provided a systematic approach to quantifying bacterial plaque on teeth.

His work led to the largest and most comprehensive study of the health effects of smokeless tobacco among professional baseball players (Ernster et al. 1990).

[15][10][16] In his role as Dean of the UCSF School of Dentistry, Greene's leadership during the AIDS epidemic of the 1980s led to worldwide adoption of non-discriminatory treatment of all patients regardless of sexual orientation and other potential risk factors.

[1][23] He was an active leader in Marin Covenant Church in San Rafael, California, until his final years when mobility issues limited his ability to participate.

[1][23] Greene died of natural causes at Marin General Hospital in Greenbrae, California at the age of 90, surrounded by his family.