Born in British Guiana as the son of a Scottish sugar planter, Watson (pictured, center) enrolled at the University of Glasgow where his studies included math and engineering. While there, he developed a love of football.
He first played for Maxwell FC, then Parkgrove FC and, eventually, Queen's Park (he also served as a club administrator for the latter two) . While at Queen's Park, he earned high accolades, with the 1880-81 Scottish Football Association Annual calling him "one of the very best backs we have; since joining Queen's Park has made rapid strides to the front as a player; has great speed and tackles splendidly; powerful and sure kick; well worthy of a place in any representative team."
He got his first call-up to the national team for a friendly against England, captaining Scotland in their 6-1 win. He earned two other caps in his career; both were victories as well.
After retiring in 1887 after spells with Swifts, Corinthians, and a second stint at Queen's Park, Watson moved to Australia, remaining there until his death in 1902.