Born near Champlain, New York, Curtis graduated from the United States Military Academy in 1831. He moved to Ohio, where he was a lawyer and took several other civilian jobs. During the Mexican War, he served as military governor of several occupied cities. After the war, he moved to Iowa, was the mayor of Keokuk in 1856, and served in Congress from 1857 to 1861 as a Republican. He was a supporter of eventual President Abraham Lincoln, and was considered for a cabinet position; however, after the Civil War broke out, Curtis was appointed Colonel of the 2nd Iowa Infantry on June 1, 1861. He was subsequently promoted to brigadier general, effective May 17.

After organizing the chaos in St. Louis, Missouri, Curtis was given command of the Army of the Southwest on December 25, 1861, by Major General Henry W. Halleck. Curtis moved his headquarters south to Rolla, Missouri, to solidify Union control in Arkansas. His units fought at the Battle of Pea Ridge in 1862, and in July, they captured the city of Helena, Arkansas. He was promoted to Major General for his success, effective March 21, 1862. Although in September Curtis was given command of the District of Missouri, Lincoln was soon forced to reassign him, after his abolitionist views led to conflict with the governor of Missouri.

In 1864, Curtis returned to Missouri, fighting against the Confederate invasion led by Maj. Gen. Sterling Price. When that invasion was halted at the Battle of Westport, Curtis was given a position until the end of the war on the frontier, commanding the Department of the Northwest.

After the war, he returned to Keokuk, Iowa, where he was involved with the Union advances in railroads, until his death in 1866 in Council Bluffs, Iowa. He is buried in Oakland Cemetery, Keokuk.

His son Major Henry Curtis, adjutant of Brigadier General James G. Blunt, was killed by Quantrill's Raiders.