Having joined the Warriors on a one-year-deal from English Premiership side Bristol last summer, Stortoni, nicknamed Bernie, has racked up 22 appearances so far this season, scoring three tries, and is keen to show his admiration for the city and Warriors supporters by helping Glasgow beat Edinburgh and lift the 1872 Challenge Cup this weekend.
"I have always given my best for the Glasgow shirt and I love playing for the fans and for the city," he said. "My family and I are very settled in Glasgow and I'm happy to have extended my contract.
"The fans have been great to me since I arrived so I hope this shows my commitment to them. I just can't wait to give them something to shout about this Friday."
Warriors head coach, Sean Lineen, added: "Bernie is a great team man and has been one of our players of the season.
"He's a fantastic trainer, very safe under the high ball and he gives everything his all."
Stortoni was born on 17 December 1976 in Bahia Blanca, Argentina and has won 19 caps for his country.
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland