Kelso was manager of Hibernian for one season, before taking over as manager of newly promoted Woolwich Arsenal in 1904. He managed the club for four years, during which time he took the side to the FA Cup semi-finals two seasons in a row; however, his best in the league was only seventh (in 1906-07).
With the club starting to run into financial trouble and with results declining, Kelso resigned in 1908 to returned to Scotland to manage a hotel; but was tempted back down south to become manager of Fulham in 1909. He stayed with the Cottagers for 15 years, making him their longest-serving manager. After retiring from football he ran a couple of pubs in the Hammersmith area and was chairman of the Football League Managers and Secretaries Association.
Kelso died in London, in 1935, aged 63. He is buried in East Sheen