Barca retained their Primera Division crown last weekend and the addition of Villa to an already formidable forward line ought to make it even tougher for arch rivals Real Madrid to reclaim the title.
After signing a deal which contains a 200 million euros buy-out clause, the 28-year-old said: "I hope that all Barcelona fans will be happy with my performances, I am sure that will be the case.
"I have come to a club that has won everything in recent years, so I will add my little bit to make the club better than it is now and continue that run of success.
"It is already the best team and club in the world."
Villa's arrival has led to speculation Zlatan Ibrahimovic would now be surplus to requirements after a mixed first season following his arrival from Inter Milan in a swap deal which saw Samuel Eto'o move in the opposite direction.
But Villa, top scorer in Spain's triumphant Euro 2008 campaign, is hoping he can play alongside the Sweden international.
"If you work with enthusiasm then everyone is compatible," he said.
Villa's message was echoed by Barca's technical secretary Txiki Begiristain, who added: "The season is very long and challenging and we have many quality strikers.
"Just because Villa comes does not mean Ibra will have to go.
"Ibrahimovic had a spectacular season for three-quarters of it and his future has not been discussed.
"There is no doubt that Ibra will be happy (with Villa's arrival) because it's always good to have competition and he wants the same as Villa which is to win titles."