The Prime Minister's Voyager jet was sent from RAF Lossiemouth along with the fighters this afternoon.
But the Russian aircraft turned away as they approached UK airspace so an interception wasn't needed.
The Voyager was rebranded with the Union flag to "better represent" the UK abroad at a cost of £900,000 last month.
The plane which has been dubbed Hair Force One also has a military role in refuelling jets while in the air.
The Russian planes remained in international airspace and turned away as they approached what is known as the UK Flight Information Region, north west of the Western Isles.
The Voyager returned to RAF Brize Norton in Oxfordshire and the Typhoon crews to their station in Moray.