The 22-year-old was voted Scotland's Player of the Year by his fellow professional's last season.
"This is wonderful news for the club and our supporters," Celtic chief executive Peter Lawwell told the club's official website.
"Aiden's performances in recent seasons have made him the outstanding player in Scottish football and clearly we are delighted that he has committed his long-term future to the club.
"Our priority has always been to try and keep our best players at the club and the board is delighted to support Gordon in his plans for the future by securing Aiden on this long-term agreement.
"It is particularly satisfying that Aiden has become such a success having come through the ranks of our youth development programme.
"While he himself deserves immense praise for all he has done, he is also a real tribute to all those people who have assisted his development including, of course, the great Tommy Burns."