Wickham's great-grandfather, Gen. Thomas Nelson, Jr., was one of the signatories of the Declaration of Independence and a Governor of Virginia during the American Revolutionary War. Other ancestors include Thomas "Scotch Tom" Nelson who was one of the founders of Yorktown in the late 17th century. He was also a descendant of Robert "King" Carter (1663–1732), who served as an acting royal governor of Virginia and was one of its wealthiest landowners in the late 17th and early 18th centuries. His mother was a first cousin of Robert E. Lee, whose mother Anne Hill (née Carter) Lee, was born at Shirley Plantation.
Wickham was born in Richmond, Virginia, but spent much of his youth on his father's 3,200 acre plantation, Hickory Hill, which is located about 20 miles north of Richmond and 5 miles east of Ashland in Hanover County. Hickory Hill was long an outlying appendage to Shirley Plantation, much of it having come into possession of the Carter family by a deed dated March 2, 1734.
Wickham was graduated from the University of Virginia and was admitted to the bar in 1842. He was married to Lucy Penn Taylor and had several children. He became a justice and was elected to the Virginia House of Delegates in 1849.
In 1858 he was commissioned captain of Virginia volunteer militia cavalry, and in 1861 he was elected by the people of Henrico County to the state convention as a Unionist, where he voted against the articles of secession.
Wickham was commissioned brigadier general on September 9, 1863, and put in command of Wickham's brigade of Fitzhugh Lee's division. On May 11, 1864, he fought at the Battle of Yellow Tavern. Maj. Gen. J.E.B. Stuart was mortally wounded during this engagement, with his final order being: "Order Wickham to dismount his brigade and attack." In September 1864, after the Confederate defeat at the Battle of Fisher's Hill, Wickham blocked at Milford an attempt by Maj. Gen. Philip Sheridan to encircle and destroy the Confederate forces of Maj. Gen. Jubal Anderson Early. He then attacked the Federal cavalry at Waynesboro and forced them to retreat to Bridgewater.
Wickham resigned his commission on October 5, 1864, and took his seat in the Second Confederate Congress, to which he had been elected while in the field. Recognizing that the days of the Confederacy were over, he participated in the Hampton Roads Conference in an attempt to bring an early end to the war.
In November 1865, at the conclusion of the War, he was elected president of the Virginia Central Railroad, which had been one of the most heavily damaged during the War. In 1868, when the Virginia Central merged with the Covington and Ohio Railroad to form the new Chesapeake and Ohio, Wickham was retained as the new company's president. In the new capacity, he was anxious to complete a railroad line to the Ohio River, long a dream of Virginians. However, unlike fellow Confederate officer and railroad leader William Mahone had done, he was unable to secure capital or financing in Virginia, or from Europeans. Turning to New York City, he was successful in attracting an investment group headed by Collis P. Huntington. Fresh from recent completion of the western portion of the U.S. transcontinental railroad as a member of the so called "Big Four", Huntington joined the effort, became the C&O's new president. His contacts and reputation helped obtain $15 million of funding from New York financiers for the project, which eventually cost $23 million to complete. The final spike ceremony for the 428-mile long line from Richmond to the Ohio River was held on January 29, 1873 at Hawk's Nest railroad bridge in the New River Valley, near the town of Ansted in Fayette County, West Virginia. After Huntington assumed the presidency, Wickham served as vice-president of the C&O from 1869 to 1878, when the company went into foreclosure, with Wickham as receiver. In 1878 the Chesapeake and Ohio Railroad was sold under foreclosure and reorganized as the Chesapeake and Ohio Railway Company, with Collis P. Huntington assuming the office of President of the reorganized road; Wickham was named second vice-president. Under their leadership, an additional line was extended east from Richmond through the new Church Hill Tunnel and down the Virginia Peninsula through Williamsburg to reach coal piers located on the harbor Hampton Roads, the East Coast of the United State's largest ice-free port at the small unincorporated town of Newport News in Warwick County. During the ten years from 1878 to 1888, C&O's coal resources began to be developed and shipped eastward. Coal became a staple of the C&O's business at that time, and still was over 125 years later under successor CSX Transportation. The man Wickham brought to Virginia, Collis P. Huntington, went on to develop his holdings in Newport News, where he began the Newport News Shipbuilding and Drydock Company and helped the small community become one of only two in Virginia to become an independent city without first having been an incorporated town.In modern times, Newport News, whuich merged with the former Warwick County in 1958, has grown to become one of the Seven Cities of Hampton Roads.
Throughout the years after the Civil War, while developing railroads, Wickham also maintained an active political life. He maintained his offices in Richmond and his residence in Hanover County. He was elected chairman of the Hanover County, Virginia Board of Supervisors in 1871 and as a Senator in the upper house of the Virginia General Assembly in 1883. He was an officer of the C&O and held all of these other positions at the time of his death on July 23, 1888 at his office in Richmond.