"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," Arsenal manager Arsene Wenger said on the club's website (www.arsenal.com).
"Alexis will add power, creativity and quality to our squad and we are looking forward to him joining up with us in a few weeks."
The clubs had already reached a deal in principle but were ironing out personal terms for the player who was deemed surplus to requirements at Barca by new manager Luis Enrique despite his healthy goalscoring record.
Sanchez's move to London will be a blow to Liverpool who were hoping to sign him as part of a deal taking Luis Suarez in the other direction. Sanchez had also attracted interest from Italian champions Juventus.
"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," Sanchez, who completed a medical on Thursday, said.
"I'm looking forward to meeting my new team mates and to be playing for Arsenal in the Premier League and Champions League."
Sanchez was a key member of the Chile team that shone in Brazil, reaching the World Cup last 16 before losing to the hosts on penalties. He scored two goals in four appearances.
Arsenal's lack of striking prowess has been blamed for their failure to challenge for the Premier League title since the departure of Robin van Persie to Manchester United in 2012.
Their total of 68 goals from 38 matches was the lowest of the top four last season with Frenchman Olivier Giroud scoring 16 in the league.
With Chelsea having already signed Spain striker Diego Costa from Atletico Madrid, Wenger has moved quickly in the transfer window to beef up his attacking options.
Blessed with exceptional pace and ball control, Sanchez should prove to be a popular signing for the club's fans, not to mention his new team mates.
"What a Signing!!!!! Can not wait and looking forward to playing with Alexis Sanchez!!!!!" England forward Theo Walcott said on Twitter after the news broke.
Sanchez, who grew up in Tocopilla, a grim industrial city in northern Chile, scored 39 goals in 88 La Liga games for Barcelona, helping them win one La Liga title, one King's Cup, two Spanish Super Cups, one European Super Cup and one Club World Cup.
"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 squad," Wenger said.
Sanchez is expected to make his first appearance in Arsenal colours in the pre-season Emirates Cup on Aug 2-3.
(Reporting By Tony Goodson; and Martyn Herman, editing by Pritha Sarkar)
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