Back-row forward Hogg and lock Kellock have been key players for the Scots in this year's Six Nations Championship.
But the duo have also helped Edinburgh to a successful Celtic League campaign this year after joining the club from Stirling County in 2002.
Edinburgh Gunners interim head 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 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."
But, after fellow internationals such as Chris Paterson, Mike Blair and Hugo Southwell signed new Edinburgh contracts, Hogg, 23, admits his decision was straight-forward.
He said: "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 have a great bunch of boys at Edinburgh just now."
Kellock, 24, is also convinced the club are heading in the right direction.
He added: "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."