Governor Suraporn Prommoon said that relatives escorted the two jailbreakers, Faisal Dueramae and Zulgifli Yago, to see prison officials at about 8pm on Saturday.
He had ordered Tak Bai district chief officer, kamnan and village headmen to approach relatives of the remaining jailbreakers to contact them and take them back to prison in Tak Bai.
One of the jailbreakers told an official that he was afraid that he might never his relatives again if he stayed on the run any longer.
Khok Yamoo is a temporary prison in tambon Priwan, used to detain drug inmates in rehabilitation programmes.
Most of the 16 escapees are Narathiwat residents charged with drugs offences, according to authorities.