The members of God's Army, led by the Luther and Johnny Htoo, turned themselves in on the border in Suan Phung district of Ratchaburi province, said Lieutenant Colonel Somchai Suwatsuwan of the Thai border patrol police.
The group, including nine boys and two girls, surrendered M16 assault rifles and other weapons.
God's Army first gained notoriety by giving refuge to another group of Burmese dissidents - the Vigorous Burmese Student Warriors - who were freed by the Thai authorities after taking hostages at the Burmese embassy in Bangkok in October 1999.
Several months later the Warriors seized a hospital in Ratchaburi and demanded that Bangkok send doctors to treat ethnic Karen people injured in fighting with Burmese troops.
On that occasion all the hostage takers were killed by Thai commandos.
It was unclear whether God's Army, who are Karen, took part in the hospital raid.
The Burmese army, aided by Thai forces, ejected the group from its stronghold after the raid.
They have been on the run ever since.
A photograph of the twins, then 12, circulated around the world after the incident.
