William was born on December 13, 1730 in Elizabeth, New Jersey.He graduated from Princeton in 1749, studied medicine in New York, and started his practice in Newark. He was a member of Newark's Committee of Safety in 1775 bfore he joined the Continental Army as a surgeon. He opened a hospital in Newark for wounded soldiers, and ran it throughout the Revolution. He was apponted Surgeon General for the Eastern Region in 1776, and also held that position until the war ended in 1783.
Burnet was elected to the Continental Congress in 1780 and served from December 11 until his resignation. Forced to leave this service by the press of other duties and his wife's illness, he resigned on April 1, 1781. Later that year he began serving as a judge in Essex County. He also led the New Jersey Medical Society in 1787. He died in Newark on October 7, 1791.
He married Mary Comp (1731-1781) and raised a large and successful family. Among his sons Jacob Burnet was later a United States Senator from Ohio, while Ichabod and William Jr. followed their father as Doctors. His grandson (through William Jr.), David Burnet played a prominent role in Texas struggle for independence.