The decision, announced on Thursday by the agency, comes in response to a long-standing demand from the gay rights movement in the religious country.
Centrist President Luis Guillermo Solis - elected at the beginning of April - cheered the decision.
"Costa Rica woke up to good news," Solis wrote Friday on a social network.
"I feel very satisfied with the decision by social security to authorize the enrollment of same-sex couples and the fundamental right to access at the hospital."
Solis has already sparked controversy by his outspoken support for the homosexual community, receiving at government offices a delegation from the gay rights movement last week and raising the rainbow flag for the International Day Against Homophobia.
Social security executive president Maria del Rocio Saenz said it would take 90 days to implement the new reform.
"We were really waiting for this resolution, which was a fight of many years. We will be vigilant in the application of the measure, which constitutes great progress for Costa Rica," said lawyer Marco Castillo, director of the Diversity Movement rights group.