Born on 3 October 1767 at St. James's Square, London, a son of Archibald Hamilton, 9th Duke of Hamilton, he was educated at Harrow School and at Christ Church, Oxford, where he matriculated on 4 March 1786.
He received his MA on 18 February 1789.

Hamilton was a Whig, and his political career began in 1802, when he became MP for Lancaster.
He remained in the House of Commons until 1806, when he was appointed to the Privy Council, and Ambassador to the court of St. Petersburg until 1807; additionally, he was Lord Lieutenant of Lanarkshire from 1802 to 1852.
He received the numerous titles at his father's death in 1819.
He was Lord High Steward at King William IV's coronation in 1831 and Queen Victoria's coronation in 1838, and remains the last person to have undertaken this duty twice.
He became a Knight of the Garter in 1836.
 He held the office of Grand Master Mason of the Freemasons of Scotland between 1820 and 1822.
 He held the office of President of the Highland and Agricultural Society of Scotland between 1827 and 1831.
He held the office of Trustee of the British Museum between 1834 and 1852.

He married Susan Euphemia Beckford, daughter of William Thomas Beckford and Lady Margaret Gordon, daughter of Charles Gordon, 4th Earl of Aboyne, on 26 April 1810 in London, England.

Hamilton was a well-known dandy of his day.
 An obituary notice states that "timidity and variableness of temperament prevented his rendering much service to, or being much relied on by his party ... With a great predisposition to over-estimate the importance of ancient birth ... he well deserved to be considered the proudest man in England."
He also supported Napoleon and commissioned the painting The Emperor Napoleon in His Study at the Tuileries by Jacques-Louis David.

Lord Lamington, in The Days of the Dandies, wrote of him that 'never was such a magnifico as the 10th Duke, the Ambassador to the Empress Catherine; when I knew him he was very old, but held himself straight as any grenadier.
He was always dressed in a military laced undress coat, tights and Hessian boots, &c'.
Lady Stafford in letters to her son mentioned 'his great Coat, long Queue, and Fingers cover'd with gold Rings', and his foreign appearance.
  According to another obituary, this time in Gentleman's Magazine he had 'an intense family pride'.
Born on 3 October 1767 at St. James's Square, London, a son of Archibald Hamilton, 9th Duke of Hamilton, he was educated at Harrow School and at Christ Church, Oxford, where he matriculated on 4 March 1786. He received his MA on 18 February 1789.
Hamilton was a Whig, and his political career began in 1802, when he became MP for Lancaster. He remained in the House of Commons until 1806, when he was appointed to the Privy Council, and Ambassador to the court of St. Petersburg until 1807; additionally, he was Lord Lieutenant of Lanarkshire from 1802 to 1852. He received the numerous titles at his father's death in 1819. He was Lord High Steward at King William IV's coronation in 1831 and Queen Victoria's coronation in 1838, and remains the last person to have undertaken this duty twice. He became a Knight of the Garter in 1836.  He held the office of Grand Master Mason of the Freemasons of Scotland between 1820 and 1822.  He held the office of President of the Highland and Agricultural Society of Scotland between 1827 and 1831. He held the office of Trustee of the British Museum between 1834 and 1852.
He married Susan Euphemia Beckford, daughter of William Thomas Beckford and Lady Margaret Gordon, daughter of Charles Gordon, 4th Earl of Aboyne, on 26 April 1810 in London, England.
Hamilton was a well-known dandy of his day.  An obituary notice states that "timidity and variableness of temperament prevented his rendering much service to, or being much relied on by his party ... With a great predisposition to over-estimate the importance of ancient birth ... he well deserved to be considered the proudest man in England." He also supported Napoleon and commissioned the painting The Emperor Napoleon in His Study at the Tuileries by Jacques-Louis David.
Lord Lamington, in The Days of the Dandies, wrote of him that 'never was such a magnifico as the 10th Duke, the Ambassador to the Empress Catherine; when I knew him he was very old, but held himself straight as any grenadier. He was always dressed in a military laced undress coat, tights and Hessian boots, &c'. Lady Stafford in letters to her son mentioned 'his great Coat, long Queue, and Fingers cover'd with gold Rings', and his foreign appearance.   According to another obituary, this time in Gentleman's Magazine he had 'an intense family pride'.
Alexander Hamilton, 10th Duke of Hamilton