The 1997 constitution gave ethnic Indians equal political clout as indigenous Fijians.
Fiji's president, appointed by the military after the coup, was due to address the nation later tonight.
Speight says his coup was aimed at defending the rights of indigenous Fijians threatened by the economic power of the minority Indians, who were brought in 200 years ago by British colonial masters to work in the sugar plantations.
Critics and foreign governments damned it as an assault on democracy.
The ensuing political crisis brought to a head tensions between ethnic Fijians and Indians, who make up 44 percent of Fiji's 800,000 people, and ravaged the tourism, sugar and textile industries of Fiji's 320 coral-rimmed islands.
The court, protected by a heavy army cordon in the capital Suva, rejected an appeal by the military-backed interim administration of Prime Minister Laisenia Qarase against an earlier court ruling declaring it illegal.
Suva largely went about its business as usual today, though the police and military presence was heavy.
A general anxiety was aggravated by the presence to the northwest of Fiji of tropical Cyclone Paula, which threatened to bring torrential rain, and wind gusts of up to 200 kph.
Authorities have appealed for calm and the security forces have warned they will not tolerate "trouble-makers."
Foreign diplomats said Suva had become a military barracks, but the army's grip on the jungle-clad interior was less assured.
Fiji's ethnic divide flared into confrontation before, when an Indian-dominated government was ousted in two coups in 1987.
The constitution that was drafted a decade later was seen as laying to rest racial discrimination, as it gave Indo-Fijians the same political rights as indigenous Fijians, and allowed trade union leader Chaudhry to win an election in 1999.
Chaudhry and most of his multiracial cabinet were held prisoner by Speight for 56 days. Speight is currently imprisoned on an island off Suva, awaiting trial for treason.
But many indigenous Fijians believe that the prime minister's office should be reserved for a Fijian, to safeguard the rights of the islands' original inhabitants.
Having a Fijian as president - a largely symbolic office - is guaranteed because the head of state is picked by the indigenous Great Council of Chiefs, which wields great political power.
- REUTERS
Transcripts: Fiji Court of Appeal judgment
Audio
(9 minutes, courtesy FM96)
Herald Online feature: the Fiji coup
Full text: Fiji High Court rules in favour of Chaudhry
Fiji President names new Government
Main players in the Fiji coup
The hostages
Fiji facts and figures
Images of the coup - a daily record