Charles studied civil engineering at École Polytechnique in Paris, France, and in 1832 submitted proposals for a suspension bridge across the Potomac River.. In 1842, he designed the first wire-cable suspension bridge in the United States, spanning 358 feet over the Schuylkill River at Fairmount, Philadelphia, Pennsylvania. He designed the record-breaking Wheeling suspension bridge over the Ohio River at Wheeling in 1848, and a 770-foot suspension footbridge at Niagara Falls at the same time. His other civil engineering accomplishments include improving flood control and navigation of mid-western rivers and planning the layout of railways in Virginia.
Ellet published a Report of the Overflows of the Delta of the Mississippi River, which helped to reshape New Orlean's waterfront. George Perkins Marsh published Man and Nature fourteen years later, but it was Ellet who first noted in writing that the artificial embankments created an overflowing delta. It would be decades later that his assertions were taken seriously and used in flood control decisions.