Kelso began working in field archaeology after earning an M.A. (1964) in early American history at the College of William and Mary, Williamsburg, Va. He then earned a Ph.D. (1971) in historical archaeology from Emory University, Atlanta. Kelso served as commissioner of archaeology (1971–79) for the Virginia Historic Landmarks Commission, and he studied historical sites such as colonial farms and plantations along the James River before they were lost to real-estate development. He later was a research archaeologist (1979–85) and director of archaeology (1986–93) at Monticello, the Virginia home of former U.S. president Thomas Jefferson (Jefferson, Thomas). As Kelso became an expert on colonial America, he pioneered the use of archaeology to learn about slavery during the period.

Kelso held a longtime fascination with Jamestown, and in 1993 he was named director of archaeology for the Association for the Preservation of Virginia Antiquities' Jamestown Rediscovery Project. The exact location of the original fort of the Jamestown colonists on the James River in Virginia was a mystery, and all that was known about the earliest years of the settlement came from historical accounts and documents. Although the prevailing view was that the site had been washed away by the river long ago, Kelso firmly believed that the remains of the fort still existed. He began excavations in 1994 at a location where he deduced the fort might have been, and he soon unearthed several early 17th-century objects. By late 1996 he and his staff had uncovered evidence of palisades and the foundations of other structures that confirmed the identity of the fort. Subsequent excavations recovered hundreds of thousands of artifacts (such as tools, household items, weaponry, and body armour), as well as the skeletal remains of some of the first colonists. He lectured extensively about the ongoing archaeological work at the Jamestown site and headed a summer field school at which students and outside archaeologists could participate in the excavations.

Kelso was also the author of a number of books on American archaeological projects, including Kingsmill Plantations, 1619–1800: Archaeology of Country Life in Colonial Virginia (1984), Archaeology at Monticello: Artifacts of Everyday Life in the Plantation Community (1997), and Jamestown, the Buried Truth (2006).