Medical personnel performed CPR on the two men but failed to revive them.
The overcrowded boat was carrying dozens of migrants from nearby Turkey on Sunday, the first day for the implementation of the migration agreement between the EU and Turkey. It stipulates how the new arrivals from Turkey will be processed and returned.
Some 2,500 migrants currently on Lesbos and other islands are being taken to mainland Greece where they are placed in shelters before EU-wide relocation.
Twelve dead, 21 rescued as migrant boat sinks off Greek island