The La Liga champions signed the 31-year-old Chile midfielder from Bayern Munich for a reported fee which could rise to 21 million euros (£18.73 million) and he was officially presented at the Nou Camp on Monday.
"To arrive at Barcelona is a much bigger step than Bayern," Vidal told reporters.
"I hope to be an addition who can help to win all the titles. With the confidence that the people have given me, I want to win it all.
"At 15 I promised my mother I would be one of the best. I've played for a lot of teams and now I'm arriving at the best in the world."
Vidal, who won Serie A with Juventus four times between 2012 and 2015, and the Bundesliga in each of his three seasons at Bayern, has never lifted the European Cup.
Barcelona last won the Champions League in 2015, beating Vidal's Juventus in the final, and rivals Real Madrid have won it in each of the three seasons since, twice knocking out the Chilean while at Bayern.
"I don't have accounts to settle with anybody, just my objective, which is to win the Champions League, not settle scores with Real Madrid," said Vidal.
"I hope to win three Champions Leagues in the three years I will be here."
(Reporting by Rik Sharma; Editing by Christian Radnedge)
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