John Scott was born on 4 June 1751 in Newcastle-upon-Tyne, the youngest of the six surviving children of William Scott and his second wife, Jane. William Scott enjoyed a prosperous career as a ‘hostman’ or coal factor, and at his death in 1776 was the owner of several coal barges and a public house. John began his education at the Newcastle Free Grammar school and then proceeded to Oxford University. He had been intended for the family business, but his brother William, then a tutor at University College, intervened on his behalf with their father. Accordingly, John matriculated at Oxford University and entered University College on 15 May 1766, shortly before his fifteenth birthday. The following year he was awarded a college fellowship. He received his Bachelor of Arts degree in February 1770 and his Master of Arts degree three years later. While not known as a particularly brilliant scholar at Oxford, he did win the Chancellor's prize in English in 1771 for an essay entitled, ‘On the Advantages and Disadvantages of Travel in Foreign Countries’.

Scott had almost completed his MA and was intending to pursue a career in the Church when he took the precipitous step of eloping with Elizabeth Surtees on 18 November 1772. Whatever its attractions for the young couple, the marriage was not immediately popular with either family. In particular Aubone Surtees, a wealthy Newcastle banker, had greater aspirations for his daughter than that she become the wife of a curate.