Badri Patarkatsishvili died on February 13 at the age of 52. A post mortem indicated a heart attack was the cause of death.
More than 10,000 people gathered near the former tycoon's residence in Tbilisi blocking traffic. The funeral was attended by a host of dignitaries, including Georgia's ex-president Eduard Shevardnadze, religious leaders from the Caucasus state and Israel. A private jet flew about 50 people, his former business partners, from Russia.
Earlier reports said the brothers of ex-first lady and current U.S. presidential contender Hillary Clinton were also expected to attend.
Fellow tycoon Boris Berezovsky was denied entry to the country, Georgian television reported. Another fellow businessman Andrei Lugovoi, now a Russian lawmaker, chose not to attend fearing he could be extradited to Britain, where he is wanted as a chief suspect in the Litvinenko murder case.
Patarkatsishvili made his fortune, which is estimated in unofficial reports at $12 billion, in Russia following the collapse of the Soviet Union, along with Berezovsky, who now lives in London after fleeing Russia to escape prosecution on a series of charges.
Relatives and friends carried the coffin around the residence, Arkadia, in Tbilisi laying the body to rest in the courtyard.
Patarkatsishvili ran in January's early presidential polls in Georgia, but lost to the incumbent leader Mikheil Saakashvili. The opposition said the vote was rigged.
As Patarkatsishvili was under investigation in Georgia on accusations of inciting a coup after leading street protests in early November, the billionaire was forced to campaign from London.
Some opposition politicians in the ex-Soviet state suggested Patarkatsishvili's death was "not from natural causes." Results of toxicological tests carried out at the time of his death are due in the next few weeks, British police said.
The businessman's family announced on Tuesday they had hired experts to conduct an independent probe.
Expressing his condolences to Patarkatsishvili's family, President Saakashvili said his "death is a tragedy despite the serious charges" he faced.
A unified Georgian opposition leader and an ex-minister, Giorgy Khaindrava, said "Badri Patarkatsishvili's sudden death is a huge loss for Georgians and a blow for the country's future."
