In a televised statement on Friday from the Republican Palace in the capital, Sanaa, the rebel group said that it would set up a transitional national council of 551 members to replace the dissolved legislature.
The "constitutional declaration", attended by tribal and military representatives as well as by the outgoing interior and defence ministers, came after a Wednesday deadline set by the Shia militia for political parties to resolve the crisis passed with no agreement.
The United Nations said that it would not acknowledge the announcement made on Friday afternoon, calling it a unilateral decision.
Al Jazeera's Hashem Ahelbarra, who has reported extensively from Yemen, said that "the spectacular rise of the Houthis" could further fuel sectarian tensions in the country.
"This is going to be seen by the Sunnis in the country as a Shia takeover of Yemen... [which will] definitely excacerbate the sectarian divide in the country,"
The Houthi rebels moved into Sanaa from their northern stronghold of Saada in September last year seeking a broader political partnership in running the country.
They seized the presidential palace and key government buildings on January 22, prompting President Abd Rabbu Mansour Hadi and his prime minister to tender their resignations. Hadi and his cabinet are being held under house arrest by the rebels.
Under Yemeni law, only the president can issue constitutional declarations.
UN envoy leaves to Saudi Arabia
The Houthis, who are believed to be backed by Iran, called on their supporters to take to the streets for evening celebrations, which are expected to follow the declaration. They also deployed armed men and pick-up trucks with anti-aircraft guns on main streets and around key institutions.
The development comes after days of failed talks sponsored by UN envoy to Yemen, Jamal Benomar.
Benomar reportedly left Yemen for Saudi Arabia for talks on Friday.
According to senior politicians who attended the talks, the Houthis insisted on the formation of a presidential council with representatives from northern and southern Yemen.
Yemeni parties demanded assurances that the formation of the council will go hand-in-hand with a withdrawal of Houthi forces from key institutions and the release of Hadi and Cabinet members from house arrest.
Other parties in the talks wanted the parliament convene and possibly announce early elections, which the Houthis opposed, claiming the parliament had no legitimacy and that its mandate had expired.
Mohammed al-Sabri, a top politician from a multi-party alliance called the Joint Meeting Parties, described the Houthis' actions as a "coup," predicting it would lead to "international and regional isolation of Yemen".
Last year, the UN Security Council placed two Houthi leaders and deposed President Ali Abdullah Saleh, also believed to be a main backer of the Houthis, on a sanctions list for their role in derailing Yemen's transition.