The Premier League club had long been linked with a move for the France international, with the transfer now only the subject of the formal processes after the 25-year-old completed a medical and agreed personal terms on Monday.
Giroud played a key role in Montpellier's Ligue 1 title-winning 2011-12 campaign, scoring 21 goals in 36 appearances, and Arsenal manager Arsene Wenger is over the moon with the striker's arrival at the Emirates Stadium on what is described as a long-term contract.
"We are delighted to have secured the signing of Olivier Giroud," Wenger told the club's official website. "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 deal with Arsenal commences on July 1, was equally pleased to have secured a move to the Champions League hopefuls.
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"I am delighted to be here at Arsenal and to be part of one of the great teams in English football," Giroud enthused. "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."
Giroud joins compatriots Laurent Koscielny, Bacary Sagna, Sebastien Squillaci, Abou Diaby and Francis Coquelin in London.