The court had earlier permitted the other marine, Sergeant Major Salvatore Girone, to return to Italy.
Both Latorre and Girone had killed two fishermen, suspecting them to be pirates.
A bench of Justice Anil R. Dave, Justice Kurian Joseph and Justice Amitava Roy permitted Latorre to continue to stay in Italy after the central government told the court that it had no objection provided similar conditions, as imposed on Girone, applied to him.
They also told the government to submit, every three months, a report on the progress and the status of arbitration proceedings as the lawyer for the Kerala government told the bench that as told to it, the arbitration may stretch as far as 2018.
Expressing apprehension that the arbitration may go beyond 2018, the lawyer said there are nine witnesses to the killing of two fishermen but with passage of time, they may even lose interest.
The conditions imposed on Latorre are similar to one imposed on Girone and include that he would remain under the Supreme Court's jurisdiction, will have to report to a police station in Italy on first Wednesday of every month and the Indian embassy in Rome will have to be informed about it.
He would not engage in any activity that would amount to tampering with any evidence or influence any witness.
Besides, the court said the Italian Ambassador to Italy will give a fresh undertaking that Latorre shall be made to return to India in one month after the decision of the International Arbitral Tribunal and if the Indian Supreme Court required by it.
The marine was also asked to surrender his passport when he arrives in Italy.
Latorre's stay in Italy was to end on September 30, and he had sought an extension seeking parity with Girone, who is already back in Italy on health grounds.
Wednesday's order of the top court is in continuation of April 29 order of the International Tribunal for the Law of the Sea (ITLOS) by which it had asked India and Italy to cooperate in relaxing the bail conditions of Girone so that he could return to his country during the pendency of the arbitration proceedings before it.
The tribunal is arbitration to decide the question of jurisdiction between India and Italy for trail of the two Italian marines for the murder of the fishermen during an anti-piracy mission.
The case had triggered a diplomatic row between India and Italy even as the two countries last year agreed to move to the Permanent Court of Arbitration in The Hague and abide by its decisions.
The marines were on board the Italian oil tanker "Enrica Lexie" when they killed the two Indian fishermen off the coast of Kerala on February 15, 2012.
The complaint against the marines was lodged by the owner of fishing boat "St Antony" in which the fishermen were killed when the marines opened fire on, allegedly mistaking them for pirates.
