Burwell was born in 1651 or 1652, probably in Gloucester County, the only child of Lewis Burwell (1622–1652) and Lucy Higginson Burwell. Less than a year after his father’s death, his mother married William Bernard, a member of the governor’s Council, with whom she had three children before he died on March 31, 1665. By November 1667 she had married Philip Ludwell, who became a councillor eight years later and with whom she had two children. Burwell thus grew up as part of a politically prominent, wealthy, and extended family. About 1674 he married Abigail Smith, the niece and heir of Nathaniel Bacon (1620–1692), who was also a councillor. They had four sons and six daughters before her death on November 12, 1692. Sometime between March 4, 1694, and November 21, 1695, Burwell married Martha Lear Cole, daughter of John Lear, who had served on the Council, and widow of William Cole, yet another councillor. They probably had two sons and three daughters.
Burwell made good use of the connections he gained through the profitable marriages of his mother and greatly enlarged the fortune he had inherited from his father. Already related to the powerful Ludwell family, he saw his sons and daughters marry into the Armistead, Bassett, Berkeley, Carter, and Harrison families. By the 1690s the marriage alliances were no longer one-sided. In six of the seven counties in which he paid taxes in 1704, Burwell was one of the largest landowners, and in Charles City County he owned 8,000 acres, more than any other person. He paid taxes on 26,650 acres that year and was one of the wealthiest men in Virginia. His son Nathaniel Burwell (1680–1721) lived until his death at Fairfield, the striking brick mansion that Burwell had built in the 1690s on Carter’s Creek in Gloucester County; another son, Lewis Burwell (d. 1743), lived at Kingsmill, part of the former Bacon estate in James City County; and his daughter Lucy Burwell was the object of a renowned and turbulent courtship by Francis Nicholson, but she spurned the governor and married Edmund Berkeley (d. ca. 1719), of Barn Elms in Middlesex County.
Burwell was the central figure in the rise of a prominent Virginia family. By concentrating on acquiring land and pursuing family connections, he became one of the wealthiest men of his time and maximized his descendants’ ability to succeed. Among the many evidences of his prosperity was his donation of a lavish set of communion silver to Abingdon Parish. Burwell died at his plantation on King’s Creek in York County on December 19, 1710. He was buried at Fairfield in Gloucester County, but his remains were later moved to Abingdon Church.