Edmundson was born into slavery around 1840 in Halifax County. The names of his parents are not recorded. Edmundson reported that during the Civil War he was the body servant for his owner, who served as an officer in the 53rd Virginia Infantry Regiment. The scant surviving references to Edmundson in public documents indicate that he worked as a farm laborer after the war. Sometime in the 1860s or early in the 1870s he married a woman named Maria, whose maiden name is unknown. They had no children.
In June 1869 a biracial meeting of Halifax County Conservatives selected Edmundson, another former slave, and a white man as the party’s three candidates for the House of Delegates in the upcoming election. On July 6 all three Conservatives defeated the two Republican tickets, one of which included David Canada, a member of the Convention of 1867–1868, with Edmundson receiving the second highest number of votes. One of the first African Americans to serve in the General Assembly, he was appointed to a low-ranking position on the largely inconsequential Committee on Executive Expenditures. He was seriously injured on April 27, 1870, when the third floor of the Capitol, where the Virginia Supreme Court of Appeals was crowded to hear the decision concerning Richmond‘s contested mayoral election, collapsed into the House chambers, injuring about 250 others and killing approximately 60 people.
During Edmundson’s two-year term, the assembly made significant revisions to the state’s legal code to make it conform to the new state constitution. Among the most important legislation passed was the law creating the state’s first free public school system. In what became one of the most controversial acts of that assembly, a majority of the House members, including Edmundson and most of the other black delegates, voted on March 28, 1871, for the Funding Act, which pledged the state to pay the full principal and accrued interest of its antebellum public debt.
Edmundson did not seek reelection later that year. He resided in Halifax Court House, a town later known successively as Banister, Houston, and Halifax, and there opened a barber shop, where for most of the next three decades he was probably the only barber at the county seat. In February 1887 he became janitor of the courthouse, with a yearly salary of $75. In May 1877 Edmundson purchased the house and lot where he was then living for $700. In 1880 he bought another, smaller, lot, which he sold five years later. For those purchases and other purposes Edmundson borrowed money or took out mortgages on his property, but he always repaid the loans on time and with interest. In 1887 he sold his first house and lot for $100 more than he had paid for it and in 1893 recorded the purchase of another small lot on the northern edge of town.
In October 1882 the county court fined Edmundson and another man for failing to appear in court in a case involving a third man. The nature of Edmundson’s concern in the case is not clear, but he may have served as security for the appearance of the principal in the case, who also failed to appear. Edmundson appealed for relief to the General Assembly, which in January 1884 passed a bill releasing him from the obligation to pay the $50 fine and $31.45 in court costs. In August 1887 the county court fined Edmundson $1 for failing to appear when summoned to serve on the county grand jury. That he was able to have the General Assembly release him from paying the fine and court costs and was later summoned for grand jury duty indicate that he continued to be reasonably well known and respected in the county.
In May 1924 Edmonson successfully applied for a state pension under a new law that compensated African Americans who served the Confederate military in non-combat roles during the Civil War. Edmundson’s wife, who had been blind for about five years, died in Halifax on September 23, 1927, and he died a few weeks later, on November 13, 1927. They were buried in Halifax, probably in one of the church cemeteries.