Coincidentally, it means Blair - who took over the Scotland captaincy during the 2008 RBS 6 Nations - will face three of the other captains in this year's championship.
Phil Vickery led England during the RBS 6 Nations, France were captained by Lionel Nallett and Brian O'Driscoll skippered Ireland.
Edinburgh face a difficult task to emerge from arguably the most competitive pool in the tournament, which will start in early October.
However Blair - a leading contender for the Lions captaincy next year - is confident that revitalised Edinburgh can make progress.
The Scotland scrum half, who recorded his 100th appearance for Edinburgh last December, said: "The draw means we will be coming up against some of the best club sides in Europe.
"But the general consensus amongst the squad is that we have a great chance of progressing through to the knock-out stages of the European Cup and the fact the final will be played at Murrayfield is an extra incentive for us to perform."