Rauschenberg was born October 22, 1925 as Milton Ernst Rauschenberg (he changed his first name as an adult) in Port Arthur, Texas, the son of Dora and Ernest Rauschenberg. His father was of German and Cherokee ancestry and his mother of Anglo-Saxon descent. His parents were Fundamentalist Christians. Rauschenberg studied at the Kansas City Art Institute and the Académie Julian in Paris, France, where he met the painter Susan Weil, who in the summer of 1950 became his wife. In 1948 Rauschenberg and Weil decided to attend Black Mountain College in North Carolina.

Josef Albers originally of the Bauhaus school became Rauschenberg's painting instructor at Black Mountain. Albers' preliminary courses relied on strict discipline that did not allow for any "uninfluenced experimentation". Rauschenberg described Albers as influencing him to do "exactly the reverse" of what he was being taught.

From 1949 to 1952 Rauschenberg studied with Vaclav Vytlacil and Morris Kantor at the Art Students League of New York, where he met fellow artists Knox Martin and Cy Twombly.

Rauschenberg married the painter Susan Weil in 1950. Their only child, Christopher, was born July 16, 1951. They divorced in 1953. According to a 1987 oral history by the composer Morton Feldman, after the end of his marriage, Rauschenberg had romantic relationships with fellow artists Cy Twombly and Jasper Johns. An article by scholar Jonathan D. Katz states that Rauschenberg's affair with Twombly began during his marriage to Susan Weil.

Rauschenberg died on May 12, 2008 of heart failure after his personal decision to go off life support, on Captiva Island in Florida. Rauschenberg is survived by his partner of 25 years, artist Darryl Pottorf, his former assistant. Rauschenberg is also survived by his sister, Janet Begneaud, and his son, photographer Christopher Rauschenberg.

Rauschenberg's will, filed in Probate Court on October 9, 2008, names his charitable foundation as a major beneficiary, along with Pottrof, Begneaud, Christopher Rauschenberg, his nephew Byron Richard Begneaud, and Susan Weil Kirschenbaum. The amounts to be given to the beneficiaries are not named, but the estate is "worth millions," said Pottorf, who is also executor of the estate.