The legislation was approved in the country’s lower parliament. It will now go to the Spanish Senate for a second vote.
In February Spain passed a draft law which began the process of allowing the descendants of Jews banished from Spain in 1492 to take up Spanish nationality.
The original draft of the bill included a clause that would force people seeking citizenship to give up their other nationality, but it was dropped in June 2014, paving the way for people to take Spanish as their second nationality while keeping their first.
The draft law opens two routes to citizenship to descendants of Spain's Jews. They can either be accredited as a Sephardic Jew by Spain's Federation of Jewish Communities and spend two years in the country, or - in exceptional circumstances - be granted citizenship in a discretional fashion by the Spanish government.
Spanish Jews once made up one of the largest and wealthiest Jewish communities in Western Europe.
Jewish contact with the land once known as Iberia could date back to the time of King Solomon, around 950 BC.
Sephardic Jews in Spain were able to prosper and live in relative peace under both Muslim and Christian rule until Catholics Kings Ferdinand and Isabel issued the Alhambra Decree in 1492.
This resulted in forced conversions to Catholicism, killings and expulsion of all Sephardic Jews in Spain.
The law is expected to come into force in May.