The BBC's Jonathan Head in Bangkok says Mr Abhisit will start his term in office confronting some formidable challenges.
The 44-year-old British-born politician needs to restore battered economic confidence, cool the emotional political climate, and impose his authority on a cabinet drawn up as a result of days of bargaining with his coalition partners, our correspondent says.
After the speaker of parliament had gone round and asked each of the 436 MPs to state the choice, he announced that Mr Abhisit had won and that the Democrats would be given their first chance to govern for eight years.
"Abhisit gained more than half of the vote, therefore I declare that Abhisit has been elected the new prime minister," Mr Chai said.
Protesters reacted furiously to the confirmation of Abhisit Vejjajiva as the new PM
However, correspondents say the new coalition may only last a few weeks, as by-elections will be held on 11 January to fill 29 seats held by Thaksin supporters barred from politics by the court ruling.
There are also questions about the nature of the behind-the-scenes bargaining needed to persuade Thaksin loyalists to switch sides, with lucrative cabinet posts and, allegedly, large sums of cash being offered by both sides.
Outside the parliament, about 200 supporters of the ousted government reacted furiously to what they called a "silent coup", hurling barricades at the gates and stopping MPs from leaving. Several cars had their windows broken.
Some chanted "Abhisit, army nominee", Reuters news agency reported. The military is seen as being close to the Democrats.
Most demonstrators dispersed peacefully but promised to gather again later in the day.
Months of deadlock
Earlier this month, the Constitutional Court found Mr Somchai's governing People Power Party (PPP) guilty of fraud during the last election a year ago, and banned it and two other parties in the governing coalition.
Mr Somchai and several other PPP leaders were also barred from politics for five years.
However, lawmakers from the three parties who escaped the politics ban quickly formed a new party - Puea Thai (For Thailand) - or joined other parties.
On Sunday, Mr Somchai's brother-in-law, exiled former PM Thaksin Shinawatra, accused the army of using the courts to undermine the government and warned them not to interfere in politics.
The country was stricken by months of political deadlock as anti-government protesters from the People's Alliance for Democracy (PAD) mounted a campaign to topple the PPP.
The PAD accused the PPP of being a proxy for Mr Thaksin, who was ousted in a coup in 2006.
The protest culminated in a week-long occupation of Bangkok's main international airport which left 300,000 foreign tourists stranded.
The PAD called off its action following the Constitutional Court ruling.
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