They also arrested a man from Pattani province who had kept the murder weapon.
Boat was shot once with a .38 pistol. He died of the wound later, in Vachira Phuket Hospital.
The two boys, 15-year-old A and 16-year-old B (because they are minors they may not be named), were arrested in Kathu.
Police took away two sets of clothing they believe the boys were wearing on the night of the shooting, and a Honda Wave motorcycle they are believed to have been riding when they shot Boat.
Police say that during interrogation both boys admitted to the shooting.
A said that he was driving the motorcycle, and B, who was riding pillion, shot Boat because they mistook him for a member of a rival gang.
When asked about the gun used in the shooting, the boys told police that after the shooting they had given it to a man they named as Abdulla.
This led to a third arrest, of Abdulla Masalae, 25, from Pattani, at another address in Kathu. There, police seized a homemade .38 pistol and six bullets.
Abdulla faces charge of possession of a firearm and ammunition without a license.
The two boys are still under questioning at Phuket City police station.