Greenwood went undrafted in 1944 but signed late that year with the National Football League's Cleveland Rams. He came to Cleveland before the 1945 season and began an off-season job at Thompson Products Company in its engineering department. His college degree was in psychology, and he hoped to switch to personnel work. He also worked as an assistant to Edward McKeever at Cornell University before the season started. With the Rams, Greenwood was part of a potent offense led by quarterback Bob Waterfield. The team won the 1945 NFL Championship Game by a score of 15–14 in frigid conditions at Cleveland Municipal Stadium.