Giroud, who scored 25 goals for France's unlikely title-winners last season, has been representing France at Euro 2012, and has agreed a move to the Premier League following the completion of their campaign in Poland.
The striker, 25, has completed a medical with Arsenal and will join the club in a transfer worth in the region of £13 million once the formalities of the deal have been completed.
Arsene Wenger 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.”
The striker has only played top-flight football for two seasons - scoring 33 goals in 73 Ligue 1 appearances for Montpellier - and otherwise has spells in the lower leagues with Grenoble, Istres and Tours on his CV.
He 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.”
Giroud made three appearances at Euro 2012 though he played only 32 minutes.