The Indian government had allowed them to return to Italy to vote in last month’s election.
But when they failed to return, India’s Supreme Court ruled Italy’s ambassador was barred from leaving the country.
The Italian government said it had received assurances about the men’s treatment and their human rights.
Massimiliano Latorre and Salvatore Girone are accused of shooting the fishermen off the Kerala coast in February 2012. The marines had been guarding an Italian oil tanker and said they mistook the fishermen for pirates.
The marines, who had been out on bail awaiting trial, were allowed to fly back to Italy for the February 2013 general election on condition that they returned to stand trial by March 22.
Italian ambassador Daniele Mancini gave his personal assurance that they would return within four weeks.
However, then Rome decided that they would not fly back to Delhi, arguing that India was violating international law by putting them on trial, as the shooting had taken place in international waters.
Rome proposed putting them on trial in Italy.
The day before the men’s licence was due to expire, the office of Italian PM Mario Monti issued a statement saying that the marines had agreed to return.
“The marines agreed to this decision,” the statement said, adding that it was also in the men’s interest.
President Giorgio Napolitano said he appreciated their “sense of responsibility” and said Italy would remain by their side.
The Italian foreign ministry’s decision 10 days ago not to return the two men had prompted a bitter diplomatic row, with Indian PM Manmohan Singh warning of “consequences” if it was not reversed.
Then the Delhi Supreme Court ordered Rome’s envoy not to leave the country and airports across India were put on alert to stop him flying out.
Italy said restricting its ambassador’s movements violated diplomatic conventions.
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