John Alexander Low Waddell was born on January 15, 1854 in Port Hope, Ontario, Canada to Robert Waddell (b. 1815) and Angeline E. Jones. His mother was the daughter of William Jones, late colonel of the 27th regiment and sheriff of the city of New York and a member of the State legislature in 1844.
He obtained his first degree in civil engineering from Rensselaer Polytechnic Institute in Troy, New York in 1875, and soon traveled to Canada to work with that country's Marine Department of the Dominion before spending some time with the Canadian Pacific Railway.
He returned to the United States where he designed mines for a West Virginian coal company. In 1878, he returned to Rensselaer and taught mechanics courses until 1880. Waddell then traveled west, obtaining additional degrees from McGill University in Montreal, Quebec, and spending some time working at the Raymond & Campbell firm in Council Bluffs, Iowa.
Waddell returned to the United States in 1886, founding a new design company the next year in 1887 and establishing himself in Kansas City, Missouri. Waddell took on a number of challenging projects and soon demonstrated a strong ability.
Lifting and swinging bridges had been used for generations by this time, though not on the scale we know them today. Waddell was the first to come up with a modern design, originally intended to span a short channel across Minnesota Point into the harbor of Duluth, Minnesota. His design won a contest put on by the city in 1892, but the War Department objected to the design. The city built an aerial transporter bridge in that location in 1905. In 1929, it was remodeled into the Aerial Lift Bridge, similar to Waddell's design.