The Chile international is to sign a long-term contract with the Gunners after an undisclosed fee, reported to be in the region of 30 million pounds, was struck with La Liga side Barcelona.
Sanchez, who scored 39 goals in 88 Barca appearances, underwent a medical with Arsenal on Thursday before the Premier League club confirmed the transfer.
The forward, signed by Barcelona from Udinese in 2011, impressed at the 2014 World Cup in Brazil, scoring twice in four appearances for Chile, who exited at the round of 16 stage to Brazil.
Arsenal manager Arsene Wenger said on the club’s official website: “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.
“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.”