|Adams was born on July 1, 1825, in Nashville, Tennessee, of Irish immigrant parents. Having entered the U.S. Military Academy in 1841, he graduated 25th in his class, and was commissioned 2d lieutenant in the 1st Dragoons/U.S. Regular Army. He served under Captain Philip Kearny in the Mexican War. Brevetted in 1848 for gallantry and meritorious conduct at the Battle of Santa Cruz de Rosales, he was commissioned 1st lieutenant in 1851 and promoted to captain in 1856.
Adams spent the next five years at Fort Crook, California, on frontier duty, except for two years as a recruiting officer. He resigned in 1861, then went to Tennessee to enlist in the Confederate army. As a captain of cavalry, he was placed in command at Memphis, advancing to the rank of colonel by May of 1862 and then brigadier general by December of that year.
Adams took over Brigadier General Lloyd Tilghman's command of the Mississippi infantry brigade after Tilghman's death in 1863. During the campaign to relieve Vicksburg, Adams served under Gen. Joseph E. Johnston, later joining Lieutenant General Leonidas Polk in Mississippi. Adams was transferred to the Army of Tennessee, and his brigade served during most of General John B. Hood's campaign to push Major General William T. Sherman north after the fall of Atlanta. Receiving commendation for his brave service, Adams continued with General Hood during the Franklin and Nashville Campaign, and served briefly under Major General Nathan B. Forrest.
Adams was killed in the Battle of Franklin on November 30, 1864, while leading his regiment in a forceful but unsuccessful attack on Union forces.