The "Shah Deniz 2" (SD2) development transports gas to Turkey and will eventually reach elsewhere in Europe.
It is "the starting point for the Southern Gas Corridor series of pipelines that will for the first time deliver natural gas from the Caspian Sea direct to European markets," BP said in a statement.
The pipeline bypasses Russia and has been supported by the European Union, which is keen to reduce Europe's energy dependence on Moscow.
"Together with the Southern Gas Corridor pipeline system, Shah Deniz 2 will deliver significant new energy supplies to Europe, further diversifying its sources of energy," said BP group chief executive Bob Dudley, quoted in the statement.
The general director of the Southern Gas Corridor, Afgan Isayev, said the deliveries started on Saturday.