Steedman was born in Northumberland County, Pennsylvania, in the summer of 1817, the second out of five children. Steedman would not receive any formal education while growing up. He was fifteen years old when both of his parents died, and to support his siblings he worked as a typesetter for the Lewisburg Democrat newspaper in Lewisburg. Two years later he moved to Louisville, Kentucky, and found work there again as a typesetter for the Louisville Journal. He was employed as a printer until joining the Republic of Texas Army of Sam Houston in 1835.

After fighting in the Texas War of Independence, Steedman returned to home to Pennsylvania, where he worked on a public works project as a supervisor. In 1835 Steedman moved to Ohio, desiring to become a public works contractor, but failed initially to find work for his firm. He decided to return to his newspaper roots and bought a printing press in the city of Napoleon in Henry County, Ohio, where he began publishing the Northwest Democrat newspaper in 1838. Also during this time he married Miranda Slides, and contracts for public works began to come in. Steedman prospered as a contractor, his firm building early parts of both the Wabash and Erie Canal and the Toledo, Wabash and Western Railway.

Steedman began his career in politics in 1847, serving two terms in the Ohio General Assembly. Afterwards he worked as a railroad conductor and then to went to California in 1849, prospecting for gold. In 1850 he returned to Ohio, and was on the state's board for public works from 1852 to 1857, three out of those four years serving as its president. Also during this time he was admitted to the state's Bar association and then established a law practice in Toledo. Steedman became an editor of the North - Western Democrat and Toledo Times newspaper and a major general of the 5th Division in the Ohio State Militia in 1857, holding both positions until the beginning of the American Civil War in 1861. From 1856 to 1860 he also worked as a printer to the United States Congress.

In 1860 Steedman was part of Ohio's delegation to the Democratic National Convention when it met in Charleston, South Carolina, and was an active supporter of Stephen Douglas in Baltimore, Maryland. Also in 1860, he campaigned unsuccessfully for election to the U.S. House of Representatives for the district of Toledo.

At the start of the American Civil War in 1861, Steedman chose to follow the Union cause and volunteered in the United States Army. He raised and was elected colonel of the 14th Ohio Infantry Regiment on April 27. The 14th Ohio was initially a ninety day unit, but was re-organized that fall by Steedman when their enlistments were up. Steedman was mustered out of the volunteer service on August 13, and was appointed a regular army colonel of the 14th Ohio on September 1, shortly after the regiment re-enlisted for three years. Steedman and the 14th first saw action in June during the Union victory at the Battle of Philippi in Barbour County, Virginia (now part of West Virginia).

Steedman and his regiment were then sent to serve in the Western Theater. They took part in Union victory during the Battle of Mill Springs near modern day Nancy, Kentucky, in January 1862. The 14th Ohio also participated in the Siege of Corinth at Corinth, Mississippi, in late April and early June. Steedman was promoted to the rank of brigadier general on July 17, 1862, and given brigade command in the Army of the Ohio.

Following the Union victory at the Battle of Shiloh in April 1862, Steedman and his brigade were sent to join Maj. Gen. Don Carlos Buell's army in Kentucky that fall. During the Battle of Perryville on October 8, his brigade reinforced Brig. Gen. Rousseau's division, timely filling a gap in the Union line and saving the division from being pushed from the field. Steedman would receive a high commendation from Buell in his official report of the battle.

Steedman and his brigade fought during the Battle of Stones River in December 1862 and into January 1863, with his command a part of Brig. Gen. Speed S. Fry's division of the re-named Army of the Cumberland, now under the command of Maj. Gen. William S. Rosecrans.

During the Battle of Chickamauga in Tennessee in the fall of 1863, Steedman led the vanguard of Union Maj. Gen. Gordon Granger's Reserve Corps to Maj. Gen. George Henry Thomas' aid on September 20. From his position north of the battlefield at MacAfee's Church, Granger heard the sounds of the fight to the south. Without orders from Rosecrans, Granger sent Steedman's brigade to support Thomas' last - ditch defensive effort as the rest of Rosecrans' defeated army raced for Chattanooga, Tennessee.

Steedman moved quickly and arrived about 2:30 p.m., just in time to stop Confederate Lt. Gen. James Longstreet's attempt to turn Thomas's right. Steedman is credited with "performing the most conspicuous act of personal courage recorded by any army officer during the Battle of Chickamauga" and preventing Rosecrans' defeat turning into a Union "disaster." Military historian Ezra J. Warner stated that "His heroism was virtually the salvation of the Union forces left on the field" at Chickamauga. During the fight, Steedman was wounded when his horse was shot and killed under him.

In late 1863, Steedman participated in the Siege of Chattanooga, as well as the Third Battle of Chattanooga from November 23 – 25. He remained in Chattanooga, commanding all forces there until May 1864, during which he was promoted to the rank of major general on April 20. Steedman also participated in much of the Atlanta Campaign, and then commanded the District of Etowah in the Department of the Cumberland from June 15 to November 29, and again from January 5, 1865.

In between his stints of district command, Steedman fought with Thomas' army during the Battle of Nashville on December 15 – 16, 1864. At Nashville Steedman led a "provisional" division consisting of 11 regiments on the Union left. He had arrived over two days from Chattanooga by rail with about 6,000 men, a collection of his own brigade plus men returning from furlough but belonging to other units. Steedman would be the only non-West Point graduate of Thomas' six chief commanders at Nashville.

A few days before the battle, Thomas found a telegram addressed to Ulysses S. Grant, now commander of all U.S. Army forces, written by Maj. Gen. John Schofield, one of his subordinates. In it Schofield complained of Thomas' slowness at attacking the Army of Tennessee, something Grant had prodded Thomas about repeatedly. Thomas turned to Steedman, who was with him at the time, and asked "Steedman, can it be possible that Schofield would send such a telegram?" to which he replied the commanding general must be able to recognize Schofield's handwriting. Thomas admitted he could and asked "Why does he send such telegrams?" Steedman smiled at his commander's innocence and replied "General Thomas, who is next in command to you in case of removal?" referring to Schofield. After a brief pause Thomas let out a quiet "Oh, I see."

Thomas ordered Steedman and his three - brigade division to make a diversionary attack at 6 a.m. on December 15, thereby keeping the Confederate Army of Tennessee's right (the corps of Maj. Gen. Benjamin F. Cheatham) occupied all day and preventing them from aiding against the main assault elsewhere. The orders were later modified to say if his diversion could be made into a successful attack, then Steedman should do so. On December 16, Thomas ordered an attack by the corps of Maj. Gen. Thomas J. Wood (along with Steedman's men) against the right of the Army of Tennessee, now held by Maj. Gen. Stephen D. Lee's corps. At noon the attack was begun, but initially was without success. Steedman's men took heavy losses in the first assaults this day, including one of his regiments, the 13th USCT Infantry, losing 221 men, the most of any regiment that day, Union or Confederate. When the rest of Thomas' force finally broke through Cheatham's men on the left as well as the Confederate center at 4 p.m., Wood and Steedman renewed their attack and helped the rest of Thomas' army overwhelm Lee's corps, driving it from the field.

After the Battle of Nashville, Steedman returned to Etowah until he was given command of the Department of Georgia, an assignment lasting from June 27 to December 10, 1865. He remained in the Army after the end of the American Civil War until resigning on August 18, 1866.

After resigning his commission from the U.S. Army, Steedman returned home to Ohio in 1866. During the administration of U.S. President Andrew Johnson, he was the collector of internal revenue at New Orleans, Louisiana, until 1869. He again returned to Toledo, became the editor of the town's Northern Ohio Democrat newspaper, and in 1870 he was elected to the Ohio State Senate.

In May 1883 he was appointed the Chief of Police in Toledo, a post he held until his death. Steedman died in Toledo, and is buried there in Woodlawn Cemetery.