Speaking ahead of today's Magners League launch in Swansea, Kellock said: "I'm really enjoying my rugby with Glasgow.
"It looks like we're going places because we have a good squad of players having signed well over the summer and we have a fantastic ground, for both players and supporters, at Firhill Arena.
"I'm originally a Glasgow guy so I'm glad to have signed for a longer period of time and to be part of this very optimistic club."
Warriors head coach Sean Lineen added: "It's great news for Glasgow Warriors and Scotland fans that Al is extending his contract with us.
"There's no doubt he will play a major part with the Scotland national team in the future and it's exciting that he has shown commitment to stay with the Warriors because he is well respected and is developing into a world class performer."