Spain's run of 24 qualifying wins was halted by France after holding them to 1-1 draw.
After their unbeaten start to the season was ended by Chelsea last weekend, the Gunners showed great character at Upton Park to recover from conceding an early goal to Mohamed Diame.
Arsenal lacked cutting edge up front in the first game since Robin van Persie's exit, drawing 0-0 with Sunderland.
Giroud completed a medical at the club on Monday and agreed terms, with his contract officially starting July 1.
The French striker, however, has said that no decision on his future will be made until after he returns from Euro 2012.
Franck Ribery scored his first international goal for more than three years and Adil Rami grabbed a late winner as France rallied to beat Iceland 3-2.
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