The coup leader has pulled out of several previous commitments to end the 53-day-old hostage crisis.
But this is the first time Speight and his rebels have made a deal, despite weeks of intense negotiations.
Speight marched to the signing ceremony at the vice-president's official residence, 1km from Parliament, with about 400 jubilant supporters, who sang hymns, clapped and waved palm fronds.
After hymns and a prayer in Fijian, head of state Commodore Frank Bainimarama signed the agreement, followed by Speight.
Mr Bainimarama hailed the accord as the start of a long journey and urged Fijians to remain united.
Under the agreement, the rebels will concede their main sticking point and allow the council to choose the president and vice-president, with the selection to be made at the meeting.
In exchange, the interim Government will be dissolved and the rebels and those responsible for other uprisings around Fiji since the coup will be granted amnesty.
Military negotiators have already agreed to most of Speight's demands, including deposing Mahendra Chaudhry, the first Fijian of Indian descent to lead the country, and scrapping the multiracial 1997 constitution.
The agreement is likely to make Fiji an international pariah. Governments, including the United States and key trading partners New Zealand, Australia and the European Union, have threatened economic sanctions unless Fiji returns to full multiracial democracy.
The accord comes after a weekend of turmoil for Fiji, with the taking of a further 28 hostages in the village of Korovou, and the setting up of roadblocks sealing off the main road between Suva and Nadi.
Those behind the uprisings said they took action to force the military to bow to Speight's demands and were taking their orders from the rebel camp.
Two police stations on the island of Vanua Levu, at Savusavu and Seaqaqa, were taken over by Speight supporters last night. Officers from both stations were taken hostage.
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