Wellesley attended Eton between 1890 and 1895, and later attended Trinity College at Cambridge. He was commissioned as a lieutenant in the 4th (Militia) battalion of the Lincolnshire Regiment on 7 July 1897, and served as Aide-de-camp to the Earl of Ranfurly, Governor of New Zealand. After the outbreak of the Second Boer War in late 1899, he joined the regular army as a second lieutenant in the Grenadier Guards on 17 January 1900, and was part of a detachment sent to South Africa in March 1900 to reinforce the 3rd battalion fighting in the war. He served with his regiment there until July 1902, when he returned home after the war ended the previous month. He resigned his commission in 1903. He returned to active service as a temporary reserve second lieutenant in 1915, during World War I, and relinquished his commission in 1919, still a second lieutenant.