William A. Stone was born in Delmar Township, Tioga County. His father, Israel Stone, was a farmer, and his mother was Amanda Howe, a Presbyterian. Too poor to attend school, young William worked on his father's farm, garnering what little education he could on his own.

As a teenager, Stone had a strong desire to join the military. In August 1863, following the July victory of the Union Army at Gettysburg, Stone sought his chance at enlistment. An earlier biography states that "at the age of 17 he ran away to Harrisburg to volunteer, but was discharged when his father intervened." However, when Stone turned eighteen, he signed up again and fought in Company A of the 187th Pennsylvania Volunteers. Stone fought from 1863 through 1865 and was promoted to the rank of lieutenant colonel at the siege of Petersburg.

After the war he entered Mansfield State Normal School in Tioga County. Stone studied law, was admitted to the bar in 1870, and began a practice in Wellsboro, eventually moving the practice to Pittsburgh. He served eight years in Congress and became Governor in 1898. Stone was the political choice of Matthew Quay, and the governor received intense criticism for appointing Quay to the U.S. Senate.

During his term of office Stone eliminated a three million dollar debt by recalling back loans owed to the Commonwealth. It was largely this money that was used to finance the construction of the new Capitol building designed by Joseph Huston in 1902.

Governor Stone served as President of the Capitol Building Commission and appointed the other members of the commission, who oversaw the construction of the Capitol building until its completion in 1906. Though he was a Quay Republican, he engendered none of the same blame that other public officials did from the Capitol graft scandal.

After his term of office was over in 1904, Stone returned to his law practice with his son and served as the prothonotary of both the Supreme and Superior Courts of Pennsylvania. He passed away in 1920 at the age of seventy-four and is buried in Wellsboro, Pennsylvania.