Stortoni has made 22 appearances in his first season at the club following his summer move from Bristol.
The 31-year-old has now committed himself until the summer of 2010 and hopes to celebrate with a Celtic League win over Edinburgh at Firhill on Friday.
"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."