Burnet graduated from Princeton University in 1749, studied medicine under Dr. Staats in White Plains, New York, and started his practice in Newark, New Jersey.
Burnet was elected to the Continental Congress in 1780 and served from December 11, 1780, until his resignation on April 1, 1781, when he was forced to leave this service by the press of other duties and his wife's illness.
He was a member of The Society of the Cincinnati in the state of New Jersey, taking the seat of his brother Ichabod upon his death.
[1][2][3] He died in Newark, New Jersey, on October 7, 1791, aged 60, and was interred in that city's First Presbyterian Church Cemetery.
Among his sons by his first wife Jacob Burnet was later a United States Senator from Ohio, while Ichabod and William, Jr.[5] followed their father as doctors.