In a statement the MoD said the eight Russian Tupolev Tu-95 Bear aircraft, flying in loose formation of four pairs, were initially intercepted by the Norwegian air force.
Radar tracking
They were tracked by the Norwegian aircraft until entering the Nato area for which the UK has responsibility in the early hours of Thursday morning.
Under established Nato procedures the MoD said it launched quick reaction alert aircraft in order to identify the bombers, as is routine.
Four F3 Tornados were launched in two waves from RAF Leeming, in North Yorkshire.
A Boeing E-3D airborne warning and control aircraft and a VC-10 refuelling tanker supported the operation, the MoD said.
The Russian bombers eventually altered course to leave the Nato zone, being tracked by UK aircraft and the radar station at RAF Boulmer, Northumberland.
They were presumed to be heading back to their base.
The incident was the latest this summer in which British fighters have been used to warn off long-range Russian reconnaissance aircraft.
An MoD spokesman said: "The re-emergence of long-range flights from Russia is something the Russians are entitled to do.
"All countries have the right to maintain or up-grade and exercise their defence capabilities.
"The motivation behind any Russian military activity is a matter for the Russian government."
'Several incidents'
Earlier an MoD spokesman said the Russian bombers had approached but were not in British airspace.
Spokesman for the Norwegian armed forces, Lt Col John Inge Oegland, told the BBC the Russian bombers flew in international airspace from the Barents Sea to the Atlantic, before turning back.
Two Norwegian F-16s shadowed them on Thursday morning and another two went up later, he said.
There have been several similar incidents in recent months, Lt-Col Oegland added.
"Norway is following the increased Russian activity in the far north with interest," he told the BBC News website.
He said the Russian flights were not causing alarm in Norway. "Our systems are adequate," he said, when asked whether Norway was bolstering its security in the area.