Kellock has led the Warriors in every season since he signed from Edinburgh in 2006.
Speaking from Murrayfield where he is training with the Scotland team ahead of Sunday's RBS 6 Nations match against France, Kellock said: "We're playing good rugby, have continuously improved during my four years at the club and I can see us continuing to do that.
"Our fans are brilliant as well. They've continued to build year-on-year and that comes from success.
"We've built up a good team spirit and we work hard. That work ethic is massively important for me and the training facilities we will have next year are probably second to none in the Magners League."
Warriors head coach, Sean Lineen added: "It's fantastic that Al has signed because it shows that he is committed to Glasgow. He is at the centre of everything that is good about Glasgow.
"Al is integral to how we move forward as a group. The game has moved on a lot and he is a great captain."
A Bishopbriggs High School former pupil, "Big Al" played club rugby initially with Allan Glen's before he moved to Stirling County, from where he was awarded his first professional contract. Kellock also played district rugby for Glasgow at all four levels from under-16 to under-19.
Al's first competition appearance as Glasgow captain was against Newport Gwent Dragons at Hughenden on the Magners League's opening day, and he has continued in charge ever since.
Kellock made his first RBS 6 Nations Championship start in Scotland's victory over France at Murrayfield in February 2006. His senior Scotland debut was in the non-cap tour game against Queensland Reds on the 2004 summer tour of Australia.
He has 20 caps for Scotland and led the national side to victory over Australia during the Bank of Scotland Corporate Autumn Tests when club-mate Chris Cusiter retired from the match due to injury.
Glasgow Warriors chief executive, Kenny Baillie, concluded: "We now have a record number of Glasgow players challenging for international honours, so to have retained so many talented Scottish players here at Glasgow, and especially our captain, is fantastic news.
"I am absolutely delighted that Alastair is staying with the club. He is a top quality player with a real winning mentality that rubs off on the whole organisation.
"This is an exciting time for the Warriors. The move to our new training and medical centre at Scotstoun Stadium in June gives Alastair and the rest of squad the best possible environment to continue to train hard and challenge for silverware."
Please note: An audio interview with Alastair Kellock will be available on the official Glasgow Warriors website - glasgowwarriors.org - later today.
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