Dixon was born in Cockfield, near Bishop Auckland, County Durham in northern England in 1733, the fifth of seven children, to George Dixon and Mary Hunter. His father was a wealthy Quaker coal mine owner. Dixon became interested in astronomy and mathematics during his education at Barnard Castle; early in life he made acquaintances with mathematician William Emerson, and astronomers John Bird and Thomas Wright.
Jeremiah Dixon served as assistant to Charles Mason in 1761 when the Royal Society selected Mason to observe the transit of Venus from Sumatra. However, their passage to Sumatra was delayed, and they landed instead at the Cape of Good Hope where the transit was observed on June 6, 1761. Dixon returned to the Cape once again with Nevil Maskelyne's clock to work on experiments with gravity.
Dixon and Mason signed an agreement in 1763 with the proprietors of Pennsylvania and Maryland, Thomas Penn and Frederick Calvert, seventh Baron Baltimore, to assist with resolving a boundary dispute between the two provinces. They arrived in Philadelphia in November 1763 and began work towards the end of the year. The survey was not complete until late 1766, following which they stayed on to measure a degree of Earth's meridian on the Delmarva Peninsula in Maryland, on behalf of the Royal Society. They also made a number of gravity measurements with the same instrument that Dixon had used with Maskelyne in 1761. Before returning to England in 1768, they were both admitted to the American Society for Promoting Useful Knowledge, in Philadelphia.
Dixon sailed to Norway in 1769 with William Bayly to observe another transit of Venus. The two split up, with Dixon at Hammerfest Island and Bayly at North Cape, in order to minimize the possibility of inclement weather obstructing their measurements. Following their return to England in July, Dixon resumed his work as a surveyor in Durham. He died unmarried in Cockfield, January 22, 1779.
Jeremiah Dixon is one of the two titular characters of Thomas Pynchon's 1997 novel Mason & Dixon. The song Sailing to Philadelphia from Mark Knopfler's album of the same name, also refers to Mason and Dixon, and was inspired by Pynchon's book.