But the 2001 and 2005 Lion missed out on glory in both competitions as Toulon were beaten by Clermont Auvergne and Cardiff Blues respectively.
Toulon are now preparing for their first taste of the Heineken Cup and Wilkinson is determined to ensure his side give their all in what he sees as the best tournament in club rugby.
"There is nothing bigger in terms of club rugby and what you don't want to do is go there and look out of your depth," said Wilkinson, whose team have been drawn alongside Heineken Cup giants Munster, Magners League Champions the Ospreys and current English league leaders London Irish.
"The goal is to go there and give our best because those tournaments demand that of you which is why but you have to get the right preparation and dynamic.
"It's also a great test of your endurance as a club because you cannot afford to drop off for a second.
"I think, like last year, we will go to win everything.
"I think the French do that well, teams like Toulouse or Biarritz were fighting on both fronts last year, and when they don't quite make it in one they can turn their attention to the other.
"That's what great teams do and that's what we did last season - we got knocked out in the semis of the Top 14 last season and went straight into the European final the next week.
"If you've got games to play at the very end of the season you know you are in the right place."
Toulon begin life in the Heineken Cup with a home tie against the Ospreys on Saturday, October 9, before traveling to Thomond Park to take on Munster a week later.