The unidentified aircraft were tracked heading towards the north west coast of Scotland, prompting the air force to deploy three pairs of Typhoons from its Quick Reaction Alert programme.
Two pairs of Typhoons were dispatched from RAF Lossiemouth close to Moray in north-east Scotland, while the third flew from RAF Coningsby in Lincolnshire.
Flying in formation, two pairs approached the aircraft before withdrawing, while the third pair finished the job of forcing them to change course.
The unidentified aircraft were later revealed to be Tupolev Tu-95 Bears – Russian aircraft used both as strategic bombers and long-range maritime patrol planes.
The total number of Russian aircraft involved in the incident has not been revealed.
“This was a routine response to Russian aircraft approaching UK air space and was coordinated with several other Nato allies,” and RAF spokesman said.
RAF Lossiemouth tweeted: “At no point did these aircraft enter UK sovereign airspace.
“The Russian aircraft were shadowed by our Typhoons, along with (Quick Reaction Alert) aircraft from our @NATO partners in Norway and France.”
It added: “We are ready to respond to any unidentified aircraft and potential airborne threats, 24/7/365.”
In April last year, Typhoons from RAF Lossiemouth were scrambled twice in five days to prevent Russian military planes entering UK airspace.
During the same period, jets from RAF Coningsby were also deployed to a separate incident involving Russian aircraft.
Last summer, RAF fighter jets were deployed several times to see off Russian planes encroaching on Estonian airspace.
At the time, RAF personnel had been participating in Operation Azotize, a four-month deployment in the Baltic country, to support the Nato Baltic Air Policing mission.
Russia frequently uses its warplanes to intimidate the smaller country and test the strength of its response.