Henderson was born in Atlanta, Georgia, the son of Isaac Harmon Henderson and the former Ruth Ashley. He attended Clemson University in Clemson in northwestern South Carolina. He graduated from the University of Denver with a degree in advertising. He engaged in postgraduate work at New York University and completed the Advanced Management Program at Harvard University in Cambridge, Massachusetts. Henderson served in the United States Army during World War II.
While he was a student at the University of Denver, Henderson meet his wife, Donna Baade (1921-2012), daughter of the late Alfred and Fern Baade. She was reared on a farm near Bennet in Lancaster County in southeastern Nebraska, attended the University of Nebraska at Lincoln, and taught in the Nebraska public schools. The Hendersons had a son, James M. Henderson, Jr., of Greenville and two daughters, Linda H. Lucas and husband Arthur M. Lucas of Atlanta, Georgia, and Debbie H. DeMint and husband Jim DeMint, whom Henderson did not live to see become a Republican U.S. Representative from South Carolina's 4th congressional district and then U.S. Senator in 1999 and 2005, respectively.
Henderson was a member of Buncombe Street United Methodist Church in Greenville.
His first job in advertising was with General Foods in New York and Denver, Colorado. He was then associated for two years with an advertising agency in Denver. With a $500 loan from his wife, he opened his one-man Henderson Advertising, Inc., in his adopted city of Greenville in northwestern South Carolina. One of Henderson's first major accounts was Dow Chemical Company, formerly Texize, a firm that primarily produced industrial cleaner to textile mills, which were at that time abundant in the Greenville region. Henderson persuaded Greenville businessman Jack Greer, the founder of Texize, to package his cleaner for household use too.
1980, Henderson Advertising became the first agency outside of New York City or Chicago to be named "Advertising Agency of the Year" by Advertising Age magazine. Jack Callahan, who succeeded Henderson as president and board chairman of Henderson Advertising, recalled: "That's as good as it gets. The man was truly a legend. He is responsible for putting South Carolina and the Southeast on the national agency roster. He established the competitiveness of the advertising business in the Southeast. He was a great leader, a great motivator, a man who stuck to his principles, no matter what. He built a great legacy for us." As the company founder, Henderson had taken the lead in banning cigarette advertising by the firm.
Henderson received many honors in advertising. In 1954, he was named "Young Man of the Year" in Greenville. In 1961, he won the "Silver Medal Award" from the Advertising Federation of America. The Sales and Marketing Club named him "Salesman of the Year". He was a treasurer and regional chairman of the American Association of Advertising Agencies. Henderson was involved in Kiwanis International and the Greater Greenville Chamber of Commerce. He promoted the performing arts in Greenville through his work as a board member of Spoleto Festival USA, based in Charleston.
Henderson was a board member of the Citizens and Southern National Bank and First Federal Savings and Loan in Greenville. He was a trustee of Converse College in Spartanburg, South Carolina, and he served on the advisory board of the College of Commerce and Industry at his alma mater, Clemson University.
Henderson was assistant United States Postmaster General under Winton M. Blount of Alabama during the administration of U.S. President Richard M. Nixon. In that capacity he persuaded the National Aeronautics and Space Administration and the Apollo 11 astronauts to photograph the Moon for an image on a postage stamp. More than 140 million moon stamps were sold.
In 1970, Henderson was the unsuccessful Republican nominee for lieutenant governor of South Carolina. He lost to the Democrat Earle Morris, Jr., of Pickens. Henderson ran on the ticket headed by conservative U.S. Representative Albert Watson of South Carolina's 2nd congressional district, who lost the general election to the Democrat John C. West, the outgoing lieutenant governor, as the state swung to the left in the 1970 elections. Henderson questioned West's rhetoric: Why, he asked, had family income in South Carolina under Democrat state government declined over the previous two decades from 45th to 47th position nationally? Henderson also noted that average wages were higher in North Carolina or Georgia than in South Carolina. Henderson trailed Watson's total vote by 4,491 (.7 of 1 percent); hence virtually all Republican voters backed their party candidates for governor and lieutenant governor. Henderson received 216,745 votes (45.2 percent); Morris, 254,745 (53.3 percent). An Independent held the remaining 7,320 votes (1.5 percent).
Highly critical of Watson's campaign, the Greenville News noted that West won support from "every social, racial, and economic sector." It further urged the Republicans to field future candidates in the image of Henderson, rather than Watson.
In 1972, with Strom Thurmond seeking his second full term as a Republican U.S. Senator, Henderson managed the Nixon-Agnew reelection campaign in South Carolina. In that 1972 election, South Carolina led the nation in the percent of registered voters who cast ballots. In the previous 1968 election, Nixon and Agnew had also won the electoral votes of South Carolina, when the statewide campaign that year was managed by Joseph O. Rogers, Jr., of Manning, a former state representative who had been the GOP gubernatorial standard-bearer in 1966, the first serious Republican candidate to seek the governorship in ninety years.
In the 1980 presidential election, Henderson was an early donor to former Governor John B. Connally, Jr., of Texas, who withdrew from consideration after amassing only one delegate in the early portion of the campaign.
When Henderson retired in 1986 at the age of sixty-five under the compulsory company retirement policy that he had established, the agency had 120 employees and $100 million in advertising billings. It ranked in the top 1 percent of advertising agencies in the Southeast. Though he left the advertising end of the company, he maintained an office in one of the Henderson buildings, from which he engaged thereafter in real estate.
Henderson was inducted in 1989 into the South Carolina Business Hall of Fame. In a 1993 interview with The Greenville News, Henderson said that as a young man he never doubted he would succeed but that doing so took longer than he had expected.
Henderson died at the age of seventy-four and is interred beside his wife at Woodlawn Memorial Park in Greenville, South Carolina.