The Ministry of Defence said the planes were tracked heading for the northwest coast of Scotland.
The air force deployed three pairs of Typhoons from its Quick Reaction Alert programme, along with two pairs of Typhoons dispatched from RAF Lossiemouth near Moray in northeast Scotland, and a third pair from RAF Coningsby in Lincolnshire.
As they flew in formation, two pairs approached the aircraft before withdrawing, while the third pair forced the Russian aircraft to change course.
The Russian aircraft were later revealed to be Tupolev Tu-95 Bears, which are used both as strategic bombers and long-range maritime patrol planes.
An RAF spokesman said: "This was a routine response to Russian aircraft approaching UK airspace and was co-ordinated with several other NATO allies."
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, RAF Lossiemouth Typhoons were scrambled twice in five days to stop Russian military planes entering UK airspace.
Jets from RAF Coningsby were also deployed in a separate incident involving Russian aircraft during the same period.
RAF fighter jets were deployed several times last summer to see off Russian planes encroaching on Estonian airspace.
Airforce personnel had been deployed as part of a four-month operation in the Baltic nation supporting the NATO Baltic Air Policing mission
