Kellock's previous deal with Glasgow had a year left to run but he has now agreed a two-year extension.
He was left out of the Scotland World Cup squad, despite being part of Frank Hadden's training group over the summer.
But Lineen is confident the lock will soon be back in favour with his country and add to his 11 caps.
"It's great news for Glasgow Warriors and Scotland fans that Al is extending his contract with us," said Lineen.
"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."
The 26-year-old joined Glasgow from Edinburgh last year and insists he has never looked back.
"I'm really enjoying my rugby with Glasgow," he said.
"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."