The Supreme Court relaxed the bail conditions of Girone and allowed him to go to his country till an International Arbitral Tribunal decides the jurisdictional issue between India and Italy.
The other marine Massimiliano Latorre is already in Italy on health grounds and his stay there was recently extended by the apex court till September 30 this year.
"The (Italian) Foreign Ministry expresses satisfaction over today's decision of the Indian Supreme Court to immediately enforce The Hague Court of Arbitration's decision of 29 April, as recently requested by Italy," the ministry said in a statement.
The Italian Foreign Ministry pledged to abide by the bail conditions.
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"While waiting to finally welcome home Salvatore Girone, the Government renews its commitment to comply with the terms and conditions established by the Supreme Court of India," it said.
Italian Premier Matteo Renzi also expressed satisfaction with the Indian Supreme Court's decision.
"And we welcome marine Girone, who will be with us on June 2," he said. June 2 is Italy's Republic Day national holiday.
Renzi, who is currently in Japan for the G7 summit, has spoken to Girone, Italian news agency ANSA reported quoting sources.
The marines, who were on board ship 'Enrica Lexie', are accused of killing two Indian fishermen off the Kerala coast on February 15, 2012.
Italy and India have been making contrary claims over the right to prosecute the two Italian marines in the case.