Bourke went to Westminster to school and studied law at Christ Church College. In 1800 he married Elizabeth, the youngest daughter of John Bourke, with whom he had two sons and three daughters. His son John was an invalid and his son Richard (1812-1904) was from 1831 to 1834 his private secretary in New South Wales, before returning to England to study law. Bourke died in Limerick in Ireland in 1855 and was buried in Castleconnell.
On November 22, 1798, he joined the Grenadier Guards in the British Army, served in the Netherlands under Frederick Augustus, Duke of York and Albany, where he was wounded. He was lieutenant and captain on 25 November in 1799 and Major on 27 August 1805. In 1806 he became superintendent of the Royal Military College with the rank of lieutenant colonel. He was ordered to South America and took part in the siege of Montevideo and in an expedition against Buenos Aires. From 1812 to 1814 he was stationed in A Coruña in Galicia, Spain, and was appointed on June 4, 1814, Colonel. On 15 June 1825 he was promoted to Major General in Malta. Bourke was appointed for his services to the Lieutenant - Governor of the Eastern Districts of the Cape of Good Hope in South Africa. Bourke left the Cape in September 1828 and went in 1831 to New South Wales as governor. In 1837 he was promoted to lieutenant general and there after his return to Ireland in 1851 as a general.
Bourke was an able, but controversial governor. He was going against the inhuman treatment and punishment prisoners. He issued the "The Magistrates Act," which limited the number of lashes and limited the number of prisoners per contractor on 70th Bourke arranged adequate food rations for prisoners to. He also made it possible that this could be controlled by access to land of entrepreneurs and that accused prisoners received legal support. There are views that the repeal of the prisoners penal transportation to go back to Australia in 1840 to him and his arrangements.
Bourke, who noted that the children hardly education or very poor were in New South Wales at church -run mission stations, told the Anglican Church of Australia and the New South Wales state church that everyone is equal by the law. He supported and promoted the formation of schools.
In 1835 Bourke Australia proclaimed to Terra nullius ( no man's land ), when John Batman signed a contract, the Batman's Treaty, graduated with Aborigines on the use of 2,000 square kilometers of land. This meant that the Aborigines had no ownership rights to their traditional lands, that they could neither land nor have contractual arrangements for usages to complete it.
He named the city after Melbourne William Lamb, 2nd Viscount Melbourne, a Prime Minister of the United Kingdom. There are Bourke Street in Melbourne, located in the central business district of the city, in addition there is the town of Bourke in New South Wales. A statue of him stands in front of the Library of New South Wales in Sydney.