Hogg has played in all but five of Edinburgh's games this season with Kellock contributing in all but four. The lock has also captained the side on two occasions this year.
Edinburgh Gunners' coach Todd Blackadder said: "I'm very proud to see these two players sign again. It's absolutely excellent because they are two young players who are making huge contributions to Edinburgh's season. Both have real leadership qualities and they have worked hard for everything they have achieved in rugby.
"They began their professional careers here and through the Edinburgh system they have earned the highest honour of being capped for their country. I know they have so much more to give and their attitudes are first rate," he added.
Hogg said: "I'm very pleased to have extended my contract with Edinburgh. Our season is going very well and it's a real bonus for the squad to see so many players re-signing. There is a lot to play for in the coming seasons and we've got a great bunch of boys at Edinburgh just now."
Kellock said: "I'm really enjoying my rugby with Edinburgh and I think we are heading for big things. It's exciting times for Scotland too and I'm enjoying being part of the squad along with my Edinburgh team mates. There is a very good feeling in both squads at the moment and I'm pleased to have signed."
63x46.png){kind=logo}