Robben missed a penalty in last season's final loss to Chelsea but was the star of the show in Saturday's showpiece at Wembley as he set up Bayern's first goal and then scored the winner in a 2-1 victory over German rivals Borussia Dortmund.
Brazilian centre-back Dante was delighted to see Robben make such an important contribution and is also pleased that the supporters can enjoy success after the agony of last year.
"Arjen is a great player," Dante told ESPN Brasil.
"Regardless of the goal, he had complicated moments in the past but he works hard and deserves this title.
"He wanted to take revenge for last year's final. He scored the title-winning goal. I am very happy for him and for the club and the fans."
As well as losing to Robben's former club Chelsea in last season's final, Bayern were also defeated by Inter Milan in the 2010 showpiece.
And Dente admitted the feeling of finally winning was overwhelming, saying: "It's a moment I can't explain, the most important tournament after the World Cup.
"Bayern had been trying to win for four years."