Burwell was born in 1651 or 1652, probably in Gloucester County, the only child ofand 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 (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,Burwell was a popular member of Tidewater Virginia society, and his name appears regularly in the diary of (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. (1674–1744). Burwell became a militia major; a governor, or trustee, of the College of William and Mary; and a trustee of the city of . His name is not included on any extant list of justices of the peace, but a man of his would normally have served on the county court, and the loss of most of the Gloucester County records makes it impossible to rule this service out. In 1698 Burwell served a single term in the House of Burgesses, where he sat on the Committee for Propositions and Grievances. Membership on the governor’s Council was the highest office to which a Virginian could then realistically aspire, and it usually marked a man or his family as having reached the pinnacle of Virginia society. On September 5, 1700, the Privy Council appointed Burwell to the Council, but on October 13, 1701, he wrote to the and, citing his poor health, but perhaps also believing that his strained relationship with Nicholson would make membership on the Council unpleasant, asked to be excused from service. On May 14, 1702, the Privy Council accepted the Board of Trade’s recommendation that Burwell’s appointment as councillor be withdrawn, and he consequently never served.
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. 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.