The France international completed his move to the Emirates from Montpellier on Monday for a reported fee of €15 million, after playing a key role in the Ligue 1 side's title-winning 2011-12 campaign.
But Giroud, whose contract with Arsenal will commence on July 1, admitted the Gunners were not the only Premier League side to show a concrete interest in acquiring his services.
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Fellow London outfit Chelsea have been scouring the market for a replacement for Didier Drogba and it has emerged that Roman Abramovich wanted to bring the 25-year-old striker to Stamford Bridge.
Giroud revealed to TF1: "The choice was between Chelsea and Arsenal. I chose Arsenal because of the club's philosophy and stability.
"It is something that means a lot for me. I've always dreamed of playing in the Premier League and Arsenal are a great club with many French players."
"I adore Arsenal, Wenger really wanted me and I wasn't sure Di Matteo knows who I am."