He received a bachelor's degree in law from the National Autonomous University of Mexico (UNAM), a master's degree in law from the London School of Economics and a doctorate in law from the UNAM.
From 2 January 1985 to 2 January 1989, Carpizo McGregor served as Rector of the National Autonomous University of Mexico.
In the late 1980s he served as Minister Chief Justice of the Supreme Court of Justice of the Nation.
In June 1990 he was appointed president of the National Human Rights Commission (the first ombudsman in Mexico).
In 1993 President Carlos Salinas de Gortari designated him Attorney General, and he later became Secretary of the Interior.
In the following administration, President Ernesto Zedillo designated him Ambassador to France.