It is the first major pipeline from the vast Caspian oilfields to bypass Russian territory.
The Turkish and Georgian presidents, along with their Azeri counterpart, took part in a ceremony to lay the inaugural section of the pipeline at the Sangachal terminal, near the Azeri capital, Baku.
"This project guarantees peace, security and stability in the region, and still further unites three countries and three peoples", Azerbaijan's President Haidar Aliev said.
The three regional leaders were joined by American Energy Secretary Spencer Abraham, whose presence signalled the US Government's strong support for the project.
"This project is one of the most important energy undertakings from America's point of view as well as for this region," Mr Abraham said earlier.
He said such projects would contribute regional strength and international energy security for mutual benefit.
But speaking in New York ahead of the ceremony in Azerbaijan, Russian Foreign Minister Igor Ivanov said oil supplies coming from the Caspian were not sufficient to make the project economically viable.
And he warned against efforts to exclude Russia from regions where he said it had historical interests.
Political considerations
The Caspian Sea is thought to hold the world's third largest oil and gas reserves - much of it still untapped.
Pipeline data
Cost: $3bn
Length: 1,750km
Completion: 2004
Operation: 2005
Capacity: one million barrels/day
Transportation cost: $3.20 per barrel
The project was first proposed eight years ago, but has been delayed by arguments about whether enough oil will flow through the pipeline to make it financially viable.
The line is intended to transport more than a million barrels a day from Azerbaijan's oil fields through the Caucasus republic of Georgia to the Turkish port of Ceyhan.
The 1,750 kilometre (1,090 mile) pipeline to the Mediterranean was chosen in preference to two other routes to the Gulf, or the Black Sea, which would have taken the oil via Iran or Russia.
Both would have been shorter and cheaper, but were not politically acceptable to Washington.
Construction of the pipeline, which is estimated to cost about $3bn, is expected to be completed by early 2004, with pumping of oil due to begin the following year.
It is thought that the pipeline will eventually transport oil from Kazakhstan, too.