The 25-year-old, who formed part of France's squad at Euro 2012, passed a medical and agreed personal terms on Monday.
His move has now been made official, with all of the relevant paperwork processed.
He arrives in England with a big reputation, having netted 21 times for Montpellier last season as they swept to the Ligue 1 title.
Gunners boss Arsene Wenger is delighted to have bolstered his attacking ranks with a proven goal-getter and is backing Giroud to light up the Premier League.
He told the club's official website: "We are delighted to have secured the signing of Olivier Giroud.
"He has a very good physical presence and is exceptional in the air, with a great work ethic. We are excited about Olivier joining us and he will add an additional dimension to our attacking options next season.
"He has proved that he is capable of performing at the top level with club and country, and we saw what a big influence he was in Montpellier's championship-winning side last season.
"We all look forward to Olivier joining us and seeing him play in an Arsenal shirt."
Giroud, whose contract will begin on July 1, said: "I am delighted to be here at Arsenal and to be part of one of the great teams in English football.
"It's a huge satisfaction to join this great club and it's been a dream since I was young to play in the Premier League.
"I was attracted by the philosophy of football and Arsene Wenger's 'touch' at this club. I have always admired Arsenal with its great history and reputation, and I now hope to achieve great things here.
"I'm very proud to be a Gunner and I will give my best for all the Arsenal fans."
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