General Vanisittart was the eldest son of George Vansittart, MP, of Bisham Abbey in Berkshire, by Sarah, daughter of the Rev. Sir James Stonhouse, bart., of Radley Hall, also in Berkshire. Vice-Admiral Henry Vansittart (1777-1848) was his younger brother. Governor Henry Vansittart (1732-1770) and Professor Robert Vansittart (1728-1789) were his uncles. He was educated at Winchester College, at a military academy in Strasbourg and at Christ Church, Oxford, where he matriculated on 7th November 1785.

After obtaining a commission as an ensign in the 19th foot on 18th October 1786, he was allowed a year's leave to study military science at Brunswick and attend the Prussian manoeuvres. He became a lieutenant on 26th December 1787, exchanged to the 88th foot on 12th March 1788 and obtained a company in the 18th foot on 23rd June 1790. He joined that regiment at Gibraltar, went with it to Toulon in 1793, took part in its defence and was one of the last men to leave the place. He became a major in the New South Wales Corps on 20th November 1793 and lieutenant-colonel of the 96th on 21st February 1794. With them, he took part in the expedition to the Cape under Sir Alured Clarke in 1796. He was made a colonel in the army on 26th January 1797; but the 96th was broken up in the course of that year and, for the next three years, he was on half-pay and in the Berkshire Militia, which his uncle, Colonel Arthur Vansittart, had previously commanded.

On 10th April 1801, he became lieutenant-colonel of the 68th foot, went with them to the West Indies and was present at the capture of St. Lucia in June 1803. On 26th September, he was promoted to major-general and served on the staff in England from 1804 to 1806, and in Ireland from 1806 to 1810, when he became lieutenant-general, on 26th July. While in command of the Oxford district, he received the degree of DCL on 26th June 1806. He had been given the colonelcy of the 12th reserve battalion on 9th July 1803 and was transferred to the 1st garrison battalion on 26th February 1806. The colours of this battalion were afterwards presented to him and for many years hung in the great hall at Bisham Abbey.

He became a general on 19th July 1821 and died on 4th February 1824. On 29th October 1818, he had married Anna Maria, daughter and co-heiress of Thomas Copson of Sheppey Hall in Leicestershire. She survived him, with one son, George Henry (1828-1885), and a second son, Augustus Arthur (1824-1882), was born posthumously.