In 1939, his family, who were Jewish, fled the Nazi regime to Belgium, Vichy France, Portugal, and finally the United States in 1943, during World War II.

Once in the U.S., Greene enlisted in the United States Army and interrogated German prisoners for U.S. military intelligence.

From 1952 to 1953, Greene was a law clerk for Judge Bennett Champ Clark of the United States Court of Appeals for the District of Columbia Circuit.

He subsequently served as an Assistant United States Attorney for the District of Columbia until 1957 and chief of appeals research for the United States Department of Justice Civil Rights Division from 1957 to 1965.

The chair was established by an endowment gift of $1.5 million from telecommunications entrepreneurs David and Maria Wiegand of Orange County, California, owners of Pathfinder Communications at the time.