The 27-year-old has spent his entire career with the Scotstoun Stadium outfit and established himself as a key figure as the Warriors won the 2014-15 Pro12 title.
Horne, who has been capped 23 times by Scotland, is currently working his way back from an ankle injury and the club were keen to tie him down in the long term.
The Scot insists it was a no brainer to put pen-to-paper and feels Glasgow are a club moving in the right direction.
Horne said: "I've loved my time here and I love the club.
"I'm passionate about playing my rugby in Glasgow.
"I'm hungry to get better as a player and all the boys here are hungry to do better.
"We're going places, which was summed up this year with us making the European Rugby Champions Cup quarter-finals for the first time."