Many Sephardic Jews were killed, forced to convert to Christianity or leave at the end of the 15th Century.
Parliament paved the way for a change in citizenship laws two years ago, but the move needed Cabinet approval.
From now on, descendants of Sephardic Jews who can prove a strong link to Portugal can apply for a passport.
Proof can be brought, the government says, through a combination of surname, language spoken in the family or evidence of direct descent.
Thousands of Sephardic Jews were forced off the Iberian peninsula, first from Spain and then from Portugal.
Some of those who fled to other parts of Europe or to America continued to speak a form of Portuguese in their new communities.
The Portuguese government acknowledges that Jews lived in the region long before the Portuguese kingdom was founded in the 12th Century.
"There is no possibility to amend what was done," says Portuguese Justice Minister Paula Teixera da Cruz, adding that the law change was "an attribution of a right".
Portugal's Jewish community which once numbered in the tens of thousands has shrunk to just 1,000 - most of them Ashkenazim with roots in Eastern Europe.
Neighbouring Spain is still debating a similar law to address its treatment of Jews in the past.

Hoa Titcombe's husband James said he told Furness General Hospital staff "several times" his wife was ill.
Midwives Catherine McCullough and Gretta Dixon are accused of failing to have Mrs Titcombe assessed.
But midwife Caroline Duncan told the Nursing and Midwifery Council there was "no evidence" they knew she was ill.
Mr and Mrs Titcombe's son Joshua died of an infection in 2008, nine days after he was born.
On day two of the misconduct hearing, Ms Duncan said Ms McCullough did meet the standards expected of her.
However, she said that if the patient did tell her she was ill she should have referred her to be assessed in accordance with National Institute for Health and Care Excellence (Nice) and midwifery rules.
She also told the hearing there was also no evidence that Ms Dixon was aware Mrs Titcombe had been unwell.
It is alleged Ms Dixon failed to refer Mrs Titcombe for an assessment when she was told she had been unwell, on 26 October, 2008.
Ms McCullough faces the same allegation, as well as failing to take a urine sample to test for infection.
An independent inquiry into the University Hospitals of Morecambe Bay NHS Trust last year found 20 major failures from 2004 to 2013 at Furness General Hospital and concluded there were "lethal failures."
Eleven babies and one mother died after being cared for at the hospital during this time.
The hearing continues.
The Portuguese Cabinet has approved rules under which descendants of Jews expelled from Portugal more than 500 years ago can claim citizenship.
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A misconduct hearing has been told there was "no evidence" two midwives knew a woman was ill days before the birth of her son who later died.