The fighters were dispatched from RAF Leuchars in Fife soon after the presence of the two Russian Tupolev-95 long-range bombers, known to Nato forces as "bears", was spotted on radar yesterday.
After being contacted by the British pilots, the Russians changed course towards Scandinavia.
The incident comes amid continuing tensions between the West and Russia following the latter's invasion of Crimea in Ukraine.
A Ministry of Defence spokesman said: "Typhoon quick-reaction alert aircraft were launched from RAF Leuchars to determine the identity of unknown aircraft that approached the Nato air-policing area north of Scotland and could not be identified by other means.
"The aircraft were subsequently identified as Russian military aircraft. They remained in international airspace at all times as they are perfectly entitled to do."
He stressed: "Russian military flights have never entered UK sovereign airspace without authorisation."
Similar incidents occurred eight times last year, the spokesman added.
Defence experts have noted that Moscow uses such surveillance flights to remind the West of its military might and to probe other countries' air defence systems.
Next week, Typhoons will join other Nato warplanes in the Baltic states as the alliance trebles its air-policing forces to reassure eastern members concerned by Russian aggression.
On Tuesday, the US Government announced it was sending 600 troops to Poland and the three Baltic states of Estonia, Latvia and Lithuania to take part in forthcoming military exercises.
Meantime, the Royal Navy confirmed yesterday it had escorted a Russian destroyer as it approached British waters en route to the Atlantic.
In December, a row broke out after the Russian aircraft carrier, Admiral Kuznetsov, stopped briefly in the Outer Moray Firth to refuel.