Born on 11 February 1878 in Bournemouth, England, Oswald Watt was the youngest son of John Brown Watt, a Scot who had migrated to New South Wales in 1842 and became a successful merchant and politician, frequently representing his state on overseas missions. Oswald's Australian-born mother, Mary Jane, died when he was one and shortly afterwards the family relocated to Sydney. Oswald was sent back to England at the age of eleven to complete his schooling at Clifton College, Bristol, before going on to study at Trinity College, Cambridge, where he received a Bachelor of Arts degree in 1899. Returning to Sydney in 1900, he was commissioned as a second lieutenant in the New South Wales Scottish Rifles, a Militia unit, and in 1902 was appointed an aide-de-camp to the Governor of New South Wales. On 27 September that year, he married Muriel Williams at St. John's Anglican Church in Toorak, Victoria; the couple had one son.