The Gunners have been drawn in pool two against Gloucester, Leinster and Agen.
Gloucester finished fifth in the Guinness Premiership last season and are the current European Challenge Cup holders after beating London Irish 36-34 in May's final at The Stoop.
To add spice to the Edinburgh clash, Gunners scrum-half Rory Lawson and assistant coach Carl Hogg have just joined the English club.
Agen, who finished fifth in the French Championship, were also in the second-tier competition last year and were second in their pool behind runners-up London Irish.
They have recently bolstered their squad by signing former All Black prop Kees Meeuws from Castres.
Leinster were second in the Celtic League and reached the European Cup semi-finals last season, losing to eventual winners Munster 30-6.
Edinburgh Gunners began their 2005/06 campaign by beating the champions at the time London Wasps, 32-31.
They lost to Toulouse at home and away before beating Llanelli Scarlets at Murrayfield 33-32, to finish the pool in fourth place.
Murray is anticipating another exacting European Cup test next season while looking forward to an early reunion with his former Gunners colleagues.
He said: "It's obviously a pretty tough draw but then again, every pool is going to be hard in the Heineken Cup.
"Gloucester were on fire last year. They're always pretty big
up front but watching their games, they have good backs too so they'll get the ball and ship it out to them.
"It'll be good to play against them and see Rory [Lawson] and Hoggy [Carl Hogg] again.
"The good thing about Leinster is we've played them loads of times in the Celtic League but we also know how hard they'll be.
"Agen are one of the top French clubs but are perhaps not as good as some of the others and it makes a nice change not to be in a pool with Toulouse!
"We have to build on what we did last season and we have to believe we can beat all three clubs.
"We must win all our home games and pinch at least one away to have a chance of getting into the knock-out stages."