The 25-year-old forward agreed to a reported 13 million pound ($20 million) transfer on Monday, two days after France's exit in the European Championship quarterfinals against Spain .
Giroud, who made just three brief substitute appearances at Euro 2012, was Montpellier's top scorer with 21 goals in 36 games last season as they won the French title.
"He has a very good physical presence and is exceptional in the air, with a great work ethic," Arsenal manager Arsene Wenger said on Tuesday. "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."
Giroud has signed a "long-term" contract with Arsenal, which hasn't won the English Premier League since 2004 or any trophy since the FA Cup in 2005.
"I was attracted by the philosophy of football and Arsene Wenger's touch at this club," Giroud said. "I have always admired Arsenal with its great history and reputation, and I now hope to achieve great things here."