Coatbridge, Lanarkshire born outside right David Greenaway began his football career with Shettleston from where he signed for First Division club Woolwich Arsenal in the 1908 close season, making his Football League debut at Notts County the same September. He scored on his home debut in a defeat to Newcastle United and immediately established himself as Arsenal’s incumbent on the right flank, missing only two matches a season during his first two seasons at The Manor Ground.
He remained a regular during the following three seasons, however after Arsenal’s relegation from the First Division in 1913 and the arrival of Jock Rutherford from Newcastle United that November, Greenaway featured only occasionally in the final two seasons before the First World War forced the suspension of peacetime football in May 1915. During the War he served with The Royal Field Artillery, and after the War he returned to Highbury playing three further matches late on in the 1919-20 season. He stayed a further season at Arsenal before leaving the club in 1921 after 13 goals in 170 appearances for The Gunners to join Kent League club Margate on a free transfer, his final club before his eventual retirement.