The Chile international was heavily linked with a switch to the Emirates Stadium in recent days, and the Gunners have now finally secured the 25-year-old's services.
Sanchez is believed to have signed on for a fee in the region of £30m, making him the club's second most expensive signing of all time behind Mesut Ozil.
"I'm so happy to be joining Arsenal, a club which has a great manager, a fantastic squad of players, huge support around the world and a great stadium in London," the player told Arsenal's official website.
"I'm looking forward to meeting my new team-mates and to be playing for Arsenal in the Premier League and Champions League. I will give my best to Arsenal and want to make all the supporters happy."
Manager Arsene Wenger added that the winger is a "fantastic footballer" and claims that his new recruit will add plenty to the Gunners' attack.
"As many people have seen during the World Cup this summer, Alexis is a fantastic footballer and we are delighted that he is joining us at Arsenal Football Club," he said.
"Alexis will add power, creativity and much quality to our squad and we are all looking forward to him joining up with us in a few weeks.
"He has consistently produced top-quality performances at the highest level for a number of seasons now and we are all excited to see him integrate into the Arsenal squad. I'm sure all Arsenal supporters will join me in welcoming Alexis to our club."
Sanchez struck 39 times throughout a successful three-year spell in Catalunya, winning the Primera Division in 2013 along with the Copa del Rey in the same year.
He will join up with the Premier League outfit for their pre-season preparations in the coming weeks after helping Chile reach the second-round stage of the World Cup recently.
Sanchez, who also enjoyed spells with Udinese and Argentine giants River Plate, could make his competitive Arsenal debut in the Community Shield clash with Manchester City on August 10.