Italian marine Salvatore Girone will be able to return to Italy while his case is subject to an arbitration procedure.
The International Tribunal at the Hague that is dealing with the case has decided on Girone's return, upholding a request from Italy, the media reported on Monday.
The ruling will be made public on Tuesday, the sources said, but the foreign ministry in Rome confirmed the news.
The tribunal has called on both sides to agree on the procedure for the marine's return.
Girone and fellow marine Massimiliano Latorre are accused by India of killing two of its fisherman in 2012 during an anti - piracy mission.
"If the news is true, I'm incredibly happy, " Girone's father Michele said.
"Now I'll have to speak to my son and daughter - in - law to see whether it's true. "
The case is at the centre of a long diplomatic dispute between Rome and New Delhi.
Italy argues the marines should have immunity as they were servicemen working on a mission and that India does not have jurisdiction as the incident took place outside its territorial waters.
Italy took the case to International Tribunal after delays in the handling of the case in India.
New Delhi allowed Latorre to return to Italy for treatment after he had a stroke in 2014.