Free marriage registries can now be used to prove the legitimacy of marriages in the country.
The new law was passed by Parliament on Tuesday.
It was passed after a petition was launched by the campaign group Respect Marriage, which argued that the records were an unnecessary burden on couples.
The changes came into effect on 1 January.
The National Register of Free Marriages (NRF) will be available to individuals, families and civil partnerships, but not organisations or institutions.
The register will also include all marriages registered under a marriage certificate, which are not currently included in the NRF.
It will not be possible to get a divorce, or dissolve a marriage without a divorce certificate.
The NRF will also be available for those seeking to apply for a civil partnership, and to those seeking the cancellation of a marriage contract.
The bill includes a number of measures designed to address the concerns raised by the National Register.
These include: The requirement that applicants must provide a copy of a certified copy of the marriage certificate to the registrar within 24 hours of the appointment.