Russell was born the grandson of Lord John Russell, who had twice served as Prime Minister under Queen Victoria. Following the death of his mother (in 1874) and of his father (in 1876), Russell and his brother went to live with their grandparents. (Although Russell's father had granted custody of Russell and his brother to two atheists, Russell's grandparents had little difficulty in getting his will overturned.) Following the death of his grandfather (in 1878), Russell was raised by his grandmother, Lady Russell. Educated at first privately, and later at Trinity College, Cambridge, Russell obtained first class degrees both in mathematics and in the moral sciences.

Although elected to the Royal Society in 1908, Russell's career at Trinity appeared to come to an end in 1916 when he was convicted and fined for anti-war activities. He was dismissed from the College as a result of the conviction. (The details of the dismissal are recounted in Bertrand Russell and Trinity (1942) by G H Hardy.) Two years later Russell was convicted a second time. This time he spent six months in prison. It was while in prison that he wrote his well-received Introduction to Mathematical Philosophy (1919). He did not return to Trinity until 1944. Married four times and notorious for his many affairs, Russell also ran unsuccessfully for Parliament, in 1907, 1922, and 1923. Together with his second wife, he opened and ran an experimental school during the late 1920s and early 1930s. He became the third Earl Russell upon the death of his brother in 1931.

While teaching in the United States in the late 1930s, Russell was offered a teaching appointment at City College, New York. The appointment was revoked following a large number of public protests and a judicial decision, in 1940, which stated that he was morally unfit to teach at the College. Nine years later he was awarded the Order of Merit. He received the Nobel Prize for Literature in 1950.

During the 1950s and 1960s, Russell became something of an inspiration to large numbers of idealistic youth as a result of his continued anti-war and anti-nuclear protests. Together with Albert Einstein, he released the Russell-Einstein Manifesto in 1955, calling for the curtailment of nuclear weapons. In 1957, he was a prime organizer of the first Pugwash Conference, which brought together scientists concerned about the proliferation of nuclear weapons. He became the founding president of the Campaign for Nuclear Disarmament in 1958 and was once again imprisoned, this time in connection with anti-nuclear protests, in 1961. Upon appeal, his two-month prison sentence was reduced to one week in the prison hospital. He remained a prominent public figure until his death nine years later at the age of 97.