The "Law of Historical Memory" requires local governments to fund efforts to unearth mass graves from Spain's 1936-39 Civil War, where an estimated 30,000 people were buried.
The bill orders public buildings to remove any statues, symbols or plaques relating to Franco's rule or his Falange nationalist movement, a BBC correspondent reported from Madrid.
It also nullifies all verdicts from thousands of summary military trials during Franco's regime.
Socialist Prime Minister Jose Luis Rodriguez Zapatero made the bill's passage a government priority, as his grandfather was among those executed by Franco's forces.
The bill still requires passage by the senate, which is considered a formality, the report said.