Son of Phillip Yorke, 1st Earl of Hardwicke (1690-1764), and Margaret Cocks (d. 1761).
LL.D. from Glasgow (1752). Secretary to the Embassy at Paris (1749-1751). Minister at the Hague (1751-1761). MP for East Grinstead (1751-1761). MP for Dover (1761-74). MP for Grampound (1774-1780). British Ambassador to the States General (Holland) (1761-1780). Created Baron Dover in 1788.1
In 1783, Yorke married Christiana Charlotte Margaret de Stöcken, a daughter of Danish nobleman Johan Henrik, Baron de Stöcken, and widow of Jacob Filip, Baron van den Boetzelaer (d. 1781). Yorke died without issue in December 1792. His wife survived him for only a few months, dying in March 1793.
Boswell was introduced to Sir Joseph at the Hague on December 25, 1763, and met him several times over the next 7-8 months.