Some 700 migrants, mostly families or members of vulnerable groups, left Lesvos on Monday and boarded a ferry to the mainland.
This was the first stage of the planned relocation of 2,500 people from the eastern Aegean island.
The Nisos Chios passenger ferry then collected another 300 people from Chios, Samos, Leros and Kos.
The migrants will be housed in accommodation on the mainland as part of the Helios program which the International Organization for Migration is running in association with the Greek government.
Another 700 people are expected to leave Lesvos next Thursday, October 1.
The Migration and Asylum Ministry's goal is to move a total of 2,500 people from Lesvos by the end of next week.
It is recalled earlier this month, a fire broke out at Moria reception and registration center, nicknamed "the jungle", on the island of Lesvos, leaving about 12,000 people stranded.
Most of them have moved to the new camp on a former military firing range at Kara Tepe.
On Monday, 8,550 people remained at the new camp.