The former Whites midfielder is just six games away from guiding the side into the League One's play-offs, and the offer of fresh terms has removed any doubt over his immediate future.
The 43-year-old said in the YEP: "I'm delighted and very honoured. I was initially offered the job until the end of the season and it took me all of two seconds to agree then, and it's similar now.
"The players now know where they stand as far as I'm concerned and we can all look forward to the future together. I was very eager to stay and I want to bring success to the club."
Ken Bates added: "We've been impressed with what Gary has done and we decided it was fair to offer him a rolling contract to enable us to plan the future of Leeds United with confidence and security."
McAllister expects his assistant Steve Staunton and first-team coach Neil McDonald to follow his lead by also agreeing new deals with Leeds.
Staunton and McDonald are under contract until the summer, but McAllister confirmed: "I've recommended that they stay as part of my team. I'm sure the three of us will be here together next season."