Three Nigerians and One Indonesian were killed by firing squad shortly after midnight local time (17:00 GMT) at Nusakambangan prison island. There has been no confirmation yet from the government.
Those who were executed have been named as Indonesian Freddy Budiman, and three Nigerians - Seck Osmane, Humphrey Jefferson Ejike and Michael Titus Igweh.
10 more remain on death row to be executed. These include three other Indonesians, a Pakistani, an Indian, two other Nigerians and two Zimbabweans.
It is not clear if the remaining 10 have been spared or face being put to death in the coming days.
This, the third round of executions under President Joko Widodo.
Relatives had gathered there earlier in the day to say goodbye to loved ones, according to the Jakarta Post. It also said 17 ambulances were sent to the island - 14 of them carrying coffins.
Amnesty International condemned the executions as a "deplorable act" that violated local and international law.
Indonesia has some of the world's toughest drug laws, and has faced intense criticism internationally for resuming executions.