Team Logo. The Cleveland Rams were a team in the National Football League. They won the 1945 NFL championship in their final season. Less than a month later, they moved to California and became the Los Angeles Rams. Retrieved from "https://prosportsteams.fandom.com/wiki/Cleveland_Rams?oldid=16624" Categories: Former NFL Teams Teams in Ohio Teams in Cleveland Add category Cancel Save Community content is available under CC-BY-SA unless otherwise noted.