After the Rosenbergs were arrested, Robert and his older brother Michael lived with their maternal grandmother, Tessie Greenglass. After three months Tessie decided she was unable to care for them and the boys were sent to Hebrew Children's Home. After several months, Sophie Rosenberg, their paternal grandmother, removed them from the children's home and decided to care for the boys herself. During their stay with Sophie, the boys were allowed to visit their parents in Sing Sing prison. After one year with Sophie, the boys were sent to New Jersey to live with the Bach family, friends of the Rosenbergs. They were eventually adopted by writer and songwriter Abel Meeropol and his wife Anne, and took their last name.

In the 1960s and 1970s, Robert became active in the anti-war effort. With his brother, he also sued the FBI and CIA under the Freedom of Information Act, winning the release of 300,000 previously secret documents pertaining to his parents' case. Feeling that the documents proved their parents' innocence, Robert and Michael co-wrote a book about their childhood, We Are Your Sons: The Legacy of Ethel and Julius Rosenberg (1975). Robert followed the book in 2003 with An Execution in the Family: One Son's Journey.

Robert received undergraduate and graduate degrees in anthropology from the University of Michigan. From 1971 to 1973 he taught anthropology at Western New England College in Springfield, Massachusetts. From 1974 to 1978 he worked actively with the National Committee to reopen the Rosenberg Case and the Fund for Open Information and Accountability. From 1980 to 1982 he was managing editor of Socialist Review in the San Francisco Bay Area. In 1982 he moved back to Massachusetts and soon after enrolled in the Western New England College School of Law from which he graduated in 1985, and was admitted to the Massachusetts Bar.

In 1990, Robert started the Rosenberg Fund for Children, a public foundation which provides support for children in the U.S. whose parents are targeted, progressive activists. The RFC also supports youth in the U.S. who have been targeted for their own progressive activism.

Robert is married to Ellen Meeropol. They have two daughters: Jennifer and Rachel. Their daughter Rachel is a lawyer for the Center for Constitutional Rights in New York City.

In 2008 Michael Meeropol and Robert Meeropol stated that they now considered as a fact something they had long acknowledged as a possibility: that their father was involved in espionage with the Soviet Union. However, they continued to maintain that "To this day, there is no credible evidence that he participated in obtaining or passing on the secret of the atomic bomb, the crime for which he was executed."