Upshaw was drafted by the New York Yankees in the 5th round of the 1975 Major League Baseball Draft. Following the 1977 season, he was drafted by the Toronto Blue Jays in the rule 5 Draft. Prior to the 1988 season, Upshaw's contract was purchased by the Cleveland Indians. Upshaw is currently Major League Baseball's career leader in home runs (123) and RBIs (528) for players whose surname begins with the letter U.