Henson was born on August 8, 1866 on his parents' farm near the Potomac River in Charles County, Maryland, to sharecroppers who had been free people of color before the American Civil War. Along with many former slaves, Matthew's parents were subjected to attacks by the Ku Klux Klan and other white supremacist groups that terrorized southern blacks after the Civil War. To escape from racial violence, in 1867 the Henson family sold the farm and moved to Georgetown. He had an older sister S., born in 1864, and two younger sisters Eliza and S. Matthew's mother died when Matthew was seven. His father Lemuel remarried to a woman named Caroline and had additional children with her, including daughters and a son. After his father died, Matthew was sent to live with his uncle in Washington, D.C., who paid for a few years of education for Henson before dying. He attended a black public school for the next six years, during the last of which he took a summer job washing dishes in a restaurant. Matthew's early years were marked by one especially memorable event. When he was 10 years old, he went to a ceremony honoring Abraham Lincoln, the American President who had fought so hard to preserve the Union during the Civil War and had issued the proclamation that had freed slaves in the Confederate states in 1863. At the ceremony, Matthew was greatly inspired by a speech given by Frederick Douglass, the longtime leading figure in the American black community. A former slave turned abolitionist, Douglass called upon blacks to vigorously pursue educational opportunities and battle racial prejudice.

While working at a Washington D.C. clothing store, B.H.Stinemetz and Sons, in November 1887, Henson met Commander Robert E. Peary. Learning of Henson's sea experience, Peary recruited him as an aide for his planned voyage and surveying expedition to Nicaragua, with four other men. Peary supervised 45 Engineers on the canal survey in Nicaragua. Impressed with Henson's seamanship on that voyage, Peary recruited him as a colleague and he became "first man" in his expeditions.

During the extended expeditions to Greenland, Henson and Peary both took Inuit women as "country wives" and fathered children with them. Henson's concubine, known as Akatingwah, fathered his only child, a son named Anauakaq, born in 1906. Anauakag's children are Henson's only descendants. After 1909, Henson never saw Akatingwah or his son again; other explorers sometimes updated him about them.

His first marriage ended soon after he started on expeditions with Peary. Henson married Lucy Ross in New York City on September 7, 1907. They had no children.

Although Admiral Peary received many honors for leading the expedition to the Pole, Henson's contributions were largely ignored during the following decades. He was honored at dinners within the black community in 1909. He spent most of the next 30 years working on staff in the U.S. Customs House in New York, at the suggestion of Theodore Roosevelt.

In 1912 Matthew Henson published his memoir about his arctic explorations, A Negro Explorer at the North Pole. In his own account, he describes himself as a "general assistant, skilled craftsperson, interpreter [he had learned the Inuit language], and laborer." He later collaborated with Bradley Robinson on his 1947 biography, Dark Companion, which told more about his life.

Henson was admitted as a member to the prestigious Explorers Club in New York City in 1937, and made an honorary member in 1948, of whom there are only 20 per year. In 1944 Congress awarded him and five other Peary aides duplicates of the Peary Polar Expedition Medal, a silver medal given to Peary. Presidents Truman and Eisenhower both honored Henson before he died in 1955.

Henson died in the Bronx on March 9, 1955, at the age of 88. He was buried at Woodlawn Cemetery and survived by his wife Lucy. After her death in 1968, she was buried with him. Thirty two years after he died, his body was moved to Arlington National Cemetery.

S. Allen Counter, a neuroscientist and Director of the Harvard Foundation, had long been interested in Henson's story and traveled in Greenland for research related to it. Learning of possible descendants of the explorers, in 1986 he tracked down Henson's and Peary's sons, Anauakaq and Kali, respectively, who were then octogenarians. He arranged a visit for them the following year to the United States, where they met American relatives from both families and visited their fathers' graves. Anauakaq died in 1987. He and his wife Aviaq had five sons and a daughter, who have children of their own. They reside in Greenland.

Matthew Henson's only direct descendants were the children of his Inuit son and their children. According to S. Allen Counter, in his lifetime Henson had identified families of two nieces as being part of his extended birth family. They were Virginia Carter Brannum, daughter of Henson's sister Eliza Henson Carter of Washington, D.C., and Olive Henson Fulton of Boston, daughter of his half-brother. In a 1988 article, Counter noted that these two women had letters and photographs certifying their kinship. They were the only family members to attend Henson's funeral in 1955, with his widow Lucy Ross Henson. Counter later recommended to the United States Navy and the National Geographic Society that Audrey Mebane, daughter of Virginia Brannum, and Olive Henson Fulton be family representatives for any ceremonies honoring Henson.