The Chile international forward, who underwent a medical on Thursday afternoon, becomes the second-most expensive purchase in the Gunners' history.
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The former Udinese star will join up with his new team-mates at the end of July after spending time on holiday following the World Cup and is expected to make his first appearance for the north London club during the Emirates Cup in early August.
"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," Alexis told the club'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, meanwhile, is hopeful that his new signing can replicate his fine performances for his national team in Brazil when he begins his Premier League career.
"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," the veteran boss enthused.
"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."