The occupation had closed Suvarnabhumi international airport and the smaller domestic Don Mueang airport, stranding tens of thousands of foreign tourists and forcing them to scramble for alternative ways home.
Thailand's important tourism industry was crippled and exports of everything from electronics to fresh food were either stopped or had to be switched to ships or transported to Malaysia to be flown out.
The leaders of the anti-government People's Alliance for Democracy (PAD) said all their protests would end from 1000 (0300 GMT) on 3 December.
There are conflicting reports as to when passenger flights from the two airports will resume, but they may begin as soon as 4 December, says the BBC's Quentin Sommerville at Suvarnabhumi airport.
The date signifies the importance in the crisis of Thailand's King Bhumibol Adulyadej, whose birthday is celebrated on 5 December, our correspondent says.
Although now elderly and frail, the king is greatly revered by Thais and continues to be a powerful figurehead.
The PAD declared victory after the constitutional court's ruling forced the prime minister to step down.
Anti-government PAD protesters at the main international airport on hearing that the prime minister would step down
"The People's Alliance for Democracy has agreed to cease protesting after a long-running 192-day campaign," said Sondhi Limthongkul, one of the group's leaders.
The nine-judge constitutional court found the People Power Party (PPP), the Machima Thipatai party and the Chart Thai party guilty of vote-buying in the last general election, in 2007.
The parties have been ordered to disband and their leaders have been barred from politics for five years.
Most of the PPP's MPs will retain their seats however, and they have said they will regroup and form a new coalition.
They said they would seek a parliamentary vote for a new prime minister on 8 December.
The court's ruling came after months of PAD-led protests that have crippled the political process in Thailand.
They had vowed to continue their protests until the entire government stepped down.
They accused Mr Somchai's administration of being corrupt and hostile to the much-revered monarchy, and too close to ousted former Prime Minister Thaksin Shinawatra.
The protests had forced a political crisis, revealing deep splits between the PAD - a loose alliance of royalists, businessmen and the urban middle class - and government supporters, who draw their strength from the rural north and north-east of Thailand.
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