Born at Largs on the Firth of Clyde, Phil Kelso was manager of Hibernian for one season, 1903-04, before moving south to take up the post of manager of Woolwich Arsenal succeeding Harry Bradshaw in July 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 seventh in 1906-07.
With the club starting to run into financial trouble and with results declining, Kelso resigned in February 1908 to return to Scotland to manage a hotel, but was tempted back down south to become manager of Fulham in August 1909.
He never played professionally, although he did once turn out for Fulham in an emergency during the War at the age of 47. He stayed with the Cottagers for 15 years, throughout which time they remained a Second Division club, until May 1924, making him their longest-serving manager. He was later chairman of the Football League Managers and Secretaries Association.