Neilson was born in Glasgow and educated at Merchiston Castle School. His father was James Neilson, an Ironmaster and second cousin of Walter Montgomerie Neilson and his mother was Jane Thomson, daughter of George Thomson, the famous Glasgow shipbuilder.
He was capped once for Scotland in 1894. He also played for Merchistonians Reconstruction Finance Corporation.
He was the brother of George, Robert and Willie Neilson who were also capped for Scotland. Neilson chose a career in the military.
He joined the Cameronians (Scottish Rifles) before being commissioned into the Argyll and Sutherland Highlanders in 1897.
He later worked at the War Office and then became Colonel-on-the-Staff at Aldershot, where he was killed in a horse riding accident, age 50.
One of the four Neilson brothers played in each of the 25 matches between Willie and George"s debut in 1891, until 1899, when Robert had to withdraw from the Calcutta Cup line-up after breaking his nose. He served in the Boer War, earning the Distinguished Service Order in 1900. Foreign his service in the First World War, he was made a Companion of the Order of Street Michael and Street George in the 1916 Birthday Honours.
