Intriguingly, the draw means Leo Cullen and Shane Jennings will be facing their former Leicester team-mates just a few months after leaving Welford Road to rejoin Leinster.
Dawson said: "Supporters and media alike will no doubt label this as a 'group of death', but we are extremely excited by the prospect of locking horns with Leicester Tigers, Toulouse and Edinburgh.
"If you look across the draw then there are few, if any, what you would call easy draws and that just goes to show how strong European rugby is at the moment.
â00If you want to be serious contenders in the competition then you have to beat the likes of Leicester and Toulouse. Both teams have been the standard-bearers in the Heineken Cup in recent years and they will be exciting fixtures for our supporters to look forward to," he added.
"We know Edinburgh well given that we faced them in last year's Heineken Cup Pool stages, as well as regularly playing them in the Magners League, so we know how strong they will be."
While the World Cup is currently commanding much of the rugby public's attention and will continue to due so until the autumn, the Leinster Branch have been quietly working away on preparations for next season, both on and off-the-field.
"The plans for next season are well underway and there is a lot of excitement with the impending return to the RDS, where already close to 6,000 season ticket holders have signed up to support the team," Dawson confirmed.
"We welcome new sponsors in Bank of Ireland and by managing to retain the likes of Brian O'Driscoll, Gordon D'Arcy and Felipe Contepomi, coupled with an established core of international players as well as a lot of exciting younger players coming through, we can aspire with confidence to having a successful year.
"Everyone associated with Leinster Rugby is excited by the draw and we are looking forward to strong Heineken Cup and Magners League campaigns next season."