The youths -- Ashok Rout, Nanda Rout, Kishore Rout and Parthasarathi Nayak -- came to the Jajpur Town police station and surrendered. They had allegedly attacked Gandhi on June 20 while he was going to attend a party programme at Korei in Jajpur district.
Gandhi, who sustained injuries on his eyes and other parts of the body, had lodged an FIR with police naming the four persons.
Gandhi had also described the four youths as supporters of Korei MLA Priti Ranjan Ghadai, the son of finance minister Prafulla Ghadai.
Both the finance minister and his MLA son have denied their involvement in the attack on Gandhi.
The youths allegedly blocked Gandhi's way and attacked him and his men in the car. Later, the miscreants dragged him out of the vehicle and beat him, according to the FIR.
A case has been registered under sections 341, 323, 294,336, 363, 427 and 506 of IPC.