The Chile international was officially unveiled at Camp Nou on Monday morning, three days on from the two sides agreeing an undisclosed fee.
Vidal, who was reportedly on the brink of joining Inter Milan before Barca pounced, says that playing for the Catalan giants is something that he has always dreamed of.
"To be honest, I am very happy," he told his new side's official website. "I am looking forward to starting training with my teammates, to wearing such a famous shirt, and to doing important things here.
"It is a dream. I hope to achieve my objectives. I am here to win all the trophies available and I will give everything on the pitch to achieve this.
"[I aim on] winning everything. During the three-year contract, I hope we can win everything we play for. I am excited to play with [Lionel] Messi, [Luis] Suarez, Sergio Busquets... they are all great players."
Vidal appeared 30 times for Bayern in the Bundesliga and Champions League last season, having also previously spent four years on Juventus's books.