It was a Boeing 737-800NG from the Egyptian Airline AMC operating under Astra Airlines' routes, since their airplanes were rented for Astra continuously. The airplane got off the runway for unknown reasons till now. All 160 passengers and the Crew are safe and sound. The airplane was coming from Novosibirsk in Russia under Astra 921.
source: 11aviation.com
Astra Airlines made a public announcement and confirmed that the airplane was from another airline and that the airplane's maintanance is handled by the original airline that owns the aircraft.
Now, from my personal experience, the fact that the plane overran the runway is pretty bad, because, here in Thessaloniki Airport (LGTS) we have two runways but one of them is closed due to a current extension program. So, we have only one runway in use; one right above the sea and one which' end is about 280 meters away from a highway. I suppose that the airplane stopped from Runway 16 heading to Runway 34's start and thankfully It didn't go much further to the highway.