Hope was born at South Queensferry, West Lothian in Scotland the eldest son of the 6th Earl of Hopetoun. He was educated at Eton College and the Royal Military Academy Sandhurst, where he passed in 1879 but did not join the Army on graduation. Instead he managed the family estates and pursued a life of leisure. In 1883 he became conservative whip in the House of Lords and served as a Lord in Waiting from June 1885 to January 1886 and August 1886 to August 1889.
In 1889 he was appointed Governor of Victoria, where he served until 1895. After his return to the United Kingdom he was made a privy councillor, was appointed Paymaster-General in the Salisbury government from 1895 to 1898, and then became Lord Chamberlain until 1900. The Australian colonies had agreed to federate, to form the Commonwealth of Australia from 1 January 1901. Hopetoun's popularity in Victoria and his friendship with leading Australian politicians made him a logical choice to be the first Governor-General of the Commonwealth, and he was appointed in July 1900, arriving in Sydney on 15 December.
Hopetoun's immediate task was to appoint a Prime Minister to form an interim government, which would take office on 1 January 1901. Since the first federal elections were not scheduled to be held until March, he could not follow the usual convention of appointing the leader of the majority party in the House of Representatives. So he offered the post to Sir William Lyne, the Premier of the largest state, New South Wales.
This decision was defensible in terms of protocol, but it ignored the fact that Lyne had opposed federation and was unpopular with the leading federalist politicians. Alfred Deakin and other prominent politicians told Hopetoun they would not serve under Lyne. Eventually Lyne returned his commission and Hopetoun sent for Edmund Barton, the leader of the federal movement and the man everybody believed was entitled to the post. Hopetoun was widely criticised for this so-called "Hopetoun Blunder".
Further problems soon arose. Hopetoun had brought his own Official Secretary, Captain Edward William Wallington, who handled all his communications with London. The Australians resented an Englishman being in charge of official business. They also resented the regal pomp with which Hopetoun insisted in carrying out his role, and the expense which this entailed. He also had an unfortunate tendency to speak as though he was co-ruler of Australia beside the Prime Minister, which was not the situation the authors of the Constitution had envisaged.
An interesting friendship developed between Lord Hopetoun and the Melbourne anarchist and union pioneer, John 'Chummy' Fleming. In May 1901, Fleming protested against unemployment in Melbourne by rushing onto the Prince's Bridge to halt the Governor-General's carriage. Hopetoun told the police not to interfere, and listened to Fleming put the case for the unemployed. Out of this encounter came a friendship which endured after Hopetoun returned to England. According to some reports, Hopetoun is credited with pressuring the government to speed up government work projects.
Finally, a dispute arose over the allowance to be paid to the Governor-General to enable him to maintain vice-regal residences in both Sydney, the largest city, and Melbourne, the temporary seat of government. Rivalry between New South Wales and Victoria led to both the Commonwealth and Victorian parliaments rejecting bills to pay Hopetoun an additional allowance. As a result, Hopetoun abruptly resigned in May 1902. Hopetoun left Australia in July 1902, acutely aware that he had failed in a historic role. In compensation he was created Marquess of Linlithgow. He was Secretary for Scotland in 1905.
He died suddenly on 29 February 1908.
On 18 October 1886 he married Hersey Everleigh-de-Moleyns (31 March 1867-3 April 1937), daughter of the fourth Baron Ventry. They had four children;
While he had failed to gain the position he most wanted, Viceroy of India, his son Victor, the 2nd Marquess of Linlithgow became the longest-serving Viceroy 1936-43. His grandson Lord Glendevon married the daughter of the English novelist W. Somerset Maugham.