The three were produced before Magistrate G M Saravanakumar who remanded them in judicial custody for 15 days. They would be lodged in the high-security Puzhal Central Prison in Chennai, police said.
Earlier, the youths - identified as Vijayaraj, Prasanth and Vijayakumar - were interrogated separately by three wings of the state police - the 'Q' Branch, which deals with extremist elements, Coastal Marine Police and Intelligence Bureau officials, they said.
On a tip-off from Dhanushkodi fishermen, Marine police arrested them for entering the country without valid travel documents.
The youths told police that they were asked to leave the island by their mothers to protect themselves apprehending that Sri Lankan military could arrest and torture them.
The three alleged Sri Lankan army continued to take youths into custody.
The illegal arrival of the three youths came at a time when political parties in the state have been demanding action against Sri Lanka for 'suppression' of ethnic Tamils.