India's Supreme Court had originally refused to extend Massimiliano Latorre's leave after allowing him to spend four months in Italy to recover from cerebral ischaemia - a restricted blood supply that can lead to a stroke.
Latorre was due to return to India in January, but his lawyers approached the court in Delhi again this month seeking an extension, saying the 47-year-old marine had now undergone heart surgery.
"Considering the fact that the Union of India (government) has no objection, the time is granted to Latorre to return to India. An extension of three months' time is given," justice Anil R. Dave said.
Dave added that the Italian ambassador to India would have to sign a document assuring that Latorre would fly back in April.
Latorre and fellow marine Salvatore Girone are accused of shooting the fishermen while serving as part of an anti-piracy mission on an Italian-flagged oil tanker off the southern Indian state of Kerala in February 2012.
Girone is living at Italy's embassy in Delhi.
The Italian sailors say they mistook the fishing boat for a pirate vessel and fired what were intended to be warning shots.
Italy says the pair should be tried on home soil since the shootings involved an Italian-flagged vessel in what it insists were international waters.
India, however, maintains the killings took place in waters under its jurisdiction.
Rome last month threatened to withdraw its ambassador from India after the court rejected the appeal over the leave.
The marines were granted home visits to vote in national elections in 2013, but India was furious when the Italian government initially said it would not send the men back.
A subsequent U-turn, which followed intense Indian diplomatic pressure, triggered the resignation of Italy's then foreign minister.