Wyndham Robertson was born near Richmond, Virginia, on January 26, 1803, to William and Elizabeth Gay (Bolling) Robertson. He studied law at the College of William and Mary and was admitted to the Richmond bar in 1824. He married Mary Trigg Smith in 1831. While Robertson worked as an attorney throughout his life, his growing political convictions and devotion to the Whig party caused him to enter state politics. In 1833, he was elected to the Council of the State. Upon Governor Littleton Waller Tazewell's resignation in 1837, Robertson served as the Governor of Virginia until the election the following year. From 1838 to 1841, he served as a member of the House of Delegates in the Virignia General Assembly. Robertson then retired temporarily from politics, partially due to poor health, and moved to his wife's home, Mary's Meadows, in Abingdon, Virginia.

Though Robertson did not hold a political office again until 1859, he continued to influence politicians through personal correspondence and meetings. With the approaching American Civil War, Robertson returned to Richmond in 1858 and joined the Virginia House of Delegates again (1859-1865). In January 1861 he presented the Anti-Coercion Resolution to the House. The resolution rejected the secession of Virginia, but declared the state's willingness to join the southern cause, if the Federal Government coerced the seceded states. Following Lincoln's call for troops a few months later, which did just that, Robertson remained loyal to the Confederate cause in Virginia throughout the Civil War. He also played a vital role in re-establishing Virginia's place in the Union after the war.

Robertson retired from politics a second time around 1865 and returned to Mary's Meadows. In 1887, he published a book entitled, Pocahontas, Alias Matoaka, and Her Descendants Through Her Marriage at Jamestown, Virginia, in April, 1614, with John Rolfe, Gentleman. Robertson died in Abingdon on February 11, 1888. He is buried in Chesterfield County, Virginia.