Dr. Joshua Clayton (July 20, 1744 – August 11, 1798) was an American physician and politician from Mount Pleasant in Pencader Hundred, New Castle County, Delaware. He was an officer of the Continental Army in the American Revolution, and a member of the Federalist Party, who served in the Delaware General Assembly, as Governor of Delaware and as U.S. Senator from Delaware.

Clayton was born near Wyoming, Delaware, son of John Clayton and Eleanor Edinfield. John Clayton was a miller and the grandson of another Joshua Clayton, a Quaker who came from Lincolnshire, England, in the late 17th century.

The younger Joshua Clayton attended medical school at what is now the University of Pennsylvania in Philadelphia, from 1757 until 1762, and then began a medical practice in Middletown, Delaware. He became close friends with Richard Bassett, and in 1765, married his adopted daughter, Rachael McCleary.

Clayton acquired a portion of Bassett's Bohemia Manor estate, and in 1773 built their home, called Locust Grove. It is now known as the Dickey Farm, and is on the Choptank Road, two miles west of Mount Pleasant in Pencader Hundred, to the northwest of Middletown. There they had three children who lived to adulthood, Richard, James Lawson and Thomas. Their religious affiliation is unclear, but they were almost certainly members of the Bethel Methodist Church by the time of their deaths.

During the American Revolution, Clayton served in the Bohemia Manor militia, where he had been commissioned a major. He was also an aide and surgeon to General George Washington at the Battle of Brandywine and at Valley Forge.

Following this Clayton served in the House of Assembly in the 1778–79 session, and again from the 1780–81 session through the 1783–84 session. He was back again in the 1785–86 session, and the 1787–88 session. He was a candidate in the 1789 and 1790 elections for the U.S. House of Representatives. He was chosen President of Delaware by the Delaware General Assembly on May 30, 1789, and served as President until January 15, 1793. Under the provisions of the new Delaware Constitution of 1792 he became the first popularly elected Governor of Delaware and continued to serve in that capacity until his term ended, January 19, 1796.

This new state Constitution was the major political development of these years. With the new U.S. Constitution in place, it was necessary to revise the somewhat experimental Delaware Constitution of 1776. Under the initial leadership of John Dickinson, delegates provided for a real Governor, elected by popular vote and no longer sharing executive authority with the Privy Council. The other major change was to expand the voting franchise by eliminating the property ownership requirement.

During Clayton's tenure it was determined that a new courthouse was needed in Kent County. Since the General Assembly had moved from New Castle in 1777 it had shared the county courthouse with the county officials. They wished to continue to do so in the new building. The county commissioners responsible for erecting the building agreed, but asked for "an appropriation for the completion of the building." In response, on June 2, 1788, a committee of the General Assembly reported that "in their opinion such is the situation of the treasury, together with loud complaints of public creditors and their duty to constituents, that the prayer of the memorial cannot be complied with at this time."