Milan was barred from Europe's top club competition in July by an Italian sports tribunal investigating the country's match-fixing scandal.
UEFA's emergency panel reluctantly readmitted the team in August, saying it had "no choice" because it had no legal basis to bar it.
"Stronger than envy, injustice and bad luck. That was the slogan we coined and we've demonstrated it," Milan president Silvio Berlusconi said after Milan's 2-1 victory over Liverpool in Wednesday's final. "We're the strongest team in Europe over the last 20 years."
"We've obtained many great victories but this one is particular because it makes up for the loss two years ago and a season that didn't start off well," Berlusconi said.
Two years ago, Milan squandered a 3-0 halftime lead in the final over Liverpool to draw 3-3 and lose on penalties.
"All Italians should be grateful. In one year, we've won the World Cup and now this," Berlusconi said after Milan captain Paolo Maldini handed him the cup during the victory celebration.
The victory was a product of two goals by Filippo Inzaghi, giving him 58 in all European matches, tying him with Real Madrid's Raul Gonzalez for third place on the all-time UEFA list.
"He told me he would score two goals and he kept his promise," said Berlusconi, who called the club's training facility on Monday to speak specifically with Inzaghi and watched the players from the side of the field during their pre-final warmup at the Olympic stadium.
Berlusconi had indicated that he wanted Alberto Gilardino to start at forward, but coach Carlo Ancelotti stuck with his instincts.
"(Inzaghi) wasn't at 100 percent tonight, but he has a feeling for these games and experiences them differently from anybody else," Ancelotti said.
While he's 33, Inzaghi has the energy of a teenager, as evidenced by his wild goal celebrations. Milan captain Paolo Maldini is 38 and defense partner Alessandro Nesta is 31.
"Everyone wrote us off as old and finished but here we are and we've won again," Nesta said.
For players like Inzaghi, Nesta and right back Massimo Oddo, who played sparingly during Italy's World Cup run, this victory meant more than the one in Berlin last July.
"If I have to be sincere, the World Cup doesn't really feel like mine because I only played 22 minutes," Oddo said.
Inzaghi also made only one appearance during the World Cup, coming on to score in a first-round win over the Czech Republic. Nesta was injured against the Czechs and missed the rest of the tournament.
Virtually Milan's entire starting lineup has renewed - or plans to renew - their contracts.
"Maybe we've understood more than the other clubs how important it is to keep players even at an advanced age," Milan vice president Adriano Galliani said. "Nobody will leave this team."