Career
Born in Coatdyke, Lanarkshire, Greenaway played junior football with Shettleston before being signed at the age of 19 by London club Woolwich Arsenal in the summer of 1908. Despite his youth he was immediately propelled into the first team, making his debut against N ottinghamshire County on 2 September 1908, the first game of the 1908-1909 First Division season. He only missed two games that season and went on established himself as a regular fixture on the wing for the following four seasons.
World War I then intervened, with all league football cancelled, and Greenaway was called up to fight, serving with the Royal Field Artillery.
He returned to Arsenal in 1919 after peacetime led to the resumption of league football, but only played for the first-team three times over the next two seasons. In total he played 170 times for Arsenal, scoring 13 times, before leaving the club in 1921 on a free transfer.