Williams was an amateur artist and a member of the United States Army Corp of Engineers. He apparently was a friend of Samuel F. B. Morse who proposed him to honorary membership in the Academy. He participated in the Academy's annual exhibitions during the first half of the 1840s, showing mostly portraits, including one of Winfield Scott, and several religious works.
While in Europe acquiring books and casts for the school and library of the National Academy in 1831, Morse ran into Captain Willaim Williams who was on his second tour of Europe, the first having occured in 1821-22. In a letter written at the time to John L. Morton at the Academy, Morse referred to Williams as "a gentleman of great talent and a fine liberal man". Morse may have encouraged Williams to follow his example and acquire appropriate gifts for the Academy while in Europe, for in his letter to Morton, Morse reported that Williams was sending a "present of the `impressions from gems'" to the Academy. The gift--probably plaster casts of antique stones with carved images in relief--duly arrived, accompanied by an explanatory book or pamphlet. (In 1845, this text was translated into English by order of the Council, probably to make it more useful to students in the Academy school).
Williams died at the battle of Monterey during the Mexican-American War and the Academy's Council noted his passing thusly:
We have to lament the loss, within the past year, of. . . . Capt. W. G. Williams, U.S.A., also Honorary Member, whose eulogy has been pronounced on the battlefield of Monterey. Artist, scholar and soldier, his attachment to our cause was only equaled by his love of country, and the force of the altar is attested by the sacrifice of life. He has won a place in the regards of his country, and has left a vacancy in our ranks that few could fill so well.