Ellet was born on June 1, 1843 in Philadelphia, the son of the noted civil engineer Charles Ellet, Jr. He was studying medicine at Georgetown University when the Civil War began. He served as an Army Assistant Surgeon during 1861-62.
In the spring of 1862, when his father established the U.S. Ram Fleet, an Army unit of river steamers converted to rams, Charles Rivers Ellet transferred to that organization. Promoted to the rank of colonel later in the year, he commanded the ram Queen of the West during her daring independent operations below Vicksburg in February 1863.
While operating on the Red River and after capturing some rebel riverboats, Ellet moved the Queen upstream to investigate reports of steamships at Gordon's Landing near Marksville, Louisiana. She came under heavy fire by the shore batteries of Fort DeRussy and was run aground onto the right bank by her pilot instead of backing down river as ordered. She was directly under Confederate guns, which pounded her until Ellet ordered "abandon ship,". The Queen was not burned out of concern for the Captain of the ship who was wounded and could not be moved. In his official report, Ellet alleged the grounding was done purposely by the replacement pilot who he accused in his report of being a rebel sympathizer. During their escape downstream, the pilot also grounded the captured Era running the paddles long after contact, whereupon the pilot was placed under arrest.
Ellet was next placed in command of the ram Switzerland, in which he steamed past the Vicksburg fortifications in March 1863. He later commanded the infantry of the Mississippi Marine Brigade until his health failed.
Ellet died at Bunker Hill, Illinois.