If they fail to do so in this time, "two persons of the same sex who intend to create the said permanent union shall be allowed to have their marriage registration effectuated" the Court declared in an English translation of their decision.
In its majority opinion, the court said a provision in the current civil code barring same-sex marriages violated two articles of the constitution safeguarding human dignity and equality under the law. The justices called sexual orientation an "immutable characteristic that is resistant to change".
A draft bill on same-sex marriage is now being considered by Taiwan's legislature. Before it becomes law, it will be subject to party negotiations and must pass a second and third reading.
Taiwan could soon become the first place in Asia to legalise same-sex marriage, pending the outcome of a historic court case this Wednesday afternoon.
"What we're asking for is the equality to marry and the assurance of rights, not some other laws specifically made for same-sex couples", she said.More news: Led coalition admits 105 civilians killed in Mosul strike
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Chi Chia-wei, a 59-year-old gay rights activist, was one of the petitioners who has brought the case to the Taiwan constitutional court.
The momentum for marriage equality has been building since previous year, when President Tsai Ing-wen, openly supportive of the move, came to power.
As one of the most liberal countries in Asia, it's no surprise that Taiwan would be one of the first to legalize same-sex marriage; but nonetheless, the passing of the bill signals a big step forward for LGBT advocacy on a broader scale.
"The judges have today said yes to marriage equality".
The Committee in Taiwan's Legislature passed an amendment to include same-sex marriage in the Civil Code of the country on 26 December. The desired outcome among LGBT advocates is that same sex marriage will simply be recognized under the existing laws, but it is feared that parliament will pass new laws that treat gay marriages as civil unions, with limited rights.
The ruling follows the creation of a lobby formed in recent years by gays and lesbians in Taiwan. The ruling on Wednesday comes as the gay community is reported to be facing increasing persecution in the country.