* Saakashvili concedes his party lost parliamentary election
* Vows to respect the will of the voters
* Opposition tycoon confident of big majority in parliament (Updates results, adds quotes, details)
By Margarita Antidze and Steve Gutterman
TBILISI, Oct 2 (Reuters) - Georgian President Mikheil Saakashvili conceded on Tuesday that his ruling party had lost an election to a coalition led by billionaire Bidzina Ivanishvili, increasing the chances of a peaceful transfer of power in the former Soviet republic.
Ivanishvili said he was confident of becoming prime minister as partial results put his six-party Georgian Dream on course to win Monday's parliamentary election.
Ivanishvili's supporters streamed through Tbilisi's streets after polls closed on Monday, waving flags and sounding car horns in celebration even though Saakashvili's United National Movement (UNM) had initially claimed victory.
"According to preliminary results, it is clear that Georgian Dream obtained a majority in this election," Saakashvili, 44, said in a televised address in which he finally conceded defeat on behalf of his party.
"This means that the parliamentary majority should set up a new government, and as president, in accordance with the constitution, I will do everything to make their work comfortable, so that the parliament can choose a chairman of the parliament as well as set up a new government."
The election could mark the first peaceful transfer of power between rival parties since the Caucasus country won independence when the Soviet Union broke up in 1991.
Any instability in the nation of 4.5 million would worry the West because it is a conduit for Caspian Sea energy supplies to Europe and has a strategic location on the Black Sea between former Soviet master Russia and Iran, Turkey and central Asia.
Saakashvili will remain president until his term expires next year but governing the country could be much more difficult as he will no longer have a compliant parliament and the prime minister is likely to be his 56-year-old rival, Ivanishvili.
The U.S.-educated Saakashvili won praise for curbing corruption and implementing economic reforms, but he led Georgia into a disastrous five-day war with Russia over two breakaway regions in 2008. Opponents say he has monopolised power, mistreated opponents and trampled on rights and freedoms.
Saakashvili says the Georgian Dream coalition would move Georgia away from the West and back into Moscow's orbit, and has suggested Ivanishvili is doing the bidding of the Kremlin after making his money in Russia.
Ivanishvili denies this and accuses Saakashvili of raising the spectre of Russia to avoid addressing internal problems.
The UNM had said after the first exit polls were released on Monday that it thought it would cling to power, but its hopes faded as the official results trickled in.
"My political plan is very simple," Ivanishvili said in televised comments. "When our victory is officially confirmed, I hope ... parliament will approve me as a prime minister."
Under reforms that take effect after a presidential election next year, the authority of the head of state will be weakened and more power will go to parliament and the prime minister, who will become the most powerful executive official.
Ivanishvili, who has little experience in politics after giving up his business career only a year ago, set out plans he would pursue as prime minister, saying a balanced budget would be a priority.
He said the diverse six-party Georgian Dream might split up into as many as three factions in parliament but that "we all have a common vision on all the main issues".
Georgian Dream's strong showing was an indictment of Saakashvili, who was first elected in 2004 after the Rose Revolution - street protests over alleged fraud in a parliamentary election - toppled the post-Soviet old guard.
"I expected this result. Justice has finally been restored," I believe that Bidzina will make our lives better," said Nino Kantaria, 42, walking on Freedom Square in Tbilisi. "This is not a time for protests, it is a time for celebration." (Additional reporting by Nino Ivanishvili; Writing by Steve Gutterman, Editing by Timothy Heritage and David stamp)