Neilson was educated at Cummertrees parish school and, from January 1872 to Christmas 1873 attended King William's College on the Isle of Man.

Neilson later worked as an apprentice at a writer's office in Dumfries, and was also enrolled in the Scottish law class of Professor Robert Berry at the University of Glasgow in 1879–80.

[6] On 29 December 1909 he was appointed the first stipendiary police magistrate of Glasgow,[a] an office which he held until May 1923, when he resigned on account of ill health.

Neilson died at his home, Wellfield, 76 Partickhill Road, Partick, Glasgow, on 15 November 1923 after suffering for more than a year with stomach and bowel disease.

[11] Neilson also established relationships with numerous other scholars, in particular Mary Bateson, J. Horace Round, Andrew Lang, Francis J. Haverfield, Henry Charles Lea, and Felix Liebermann.

Outwith his traditional areas of medieval Scottish history Neilson also maintained an interest in Romano-British archaeology, a subject which he first explored in his Per lineam valli, published in 1891.

[9] Neilson wrote extensively on these particular subjects in the journal The Athenaeum and elsewhere, and in so-doing built relationships with Henry Bradley, Frederick James Furnivall, W. P. Ker, Walter William Skeat, and others.

[1] Neilson's attributions of works to the likes of Barbour and Elginton are, however, largely no longer supported or upheld by current scholars.

[1][9][12] The last 20 years of Neilson's life were predominantly spent shaping the direction of, and contributing heavily to, the Scottish Historical Review, which was founded in 1903.

[1][9] Despite his extensive scholarly activities and research output Neilson was never successful in obtaining a position within a university setting, a situation which was often lamented by his contemporaries.

Outwith these historical manuscripts the National Library of Scotland also holds select correspondence and academic papers of George Neilson.