Giroud's double took his international tally to 42 goals. He surpassed France and Juventus great Michel Platini, who had 41 goals to his name.
Now only Thierry Henry stands in front of Giroud, who scored twice in the first half against the eastern Europeans to leapfrog Platini in the standings.
It was the perfect way for Giroud to celebrate a special landmark, as he made his 100th appearance for his country against Ukraine.
The other goals came from the 17-year-old Eduardo Camavinga, who became the youngest France scorer since 1914, an own goal by Vitaliy Mykolenko, Corentin Tolisso, Kylian Mbappe and Antoine Griezmann, while Ukraine reduced the arrears through Viktor Tsygankov.
Just seven players have previously completed their century, with Lilian Thuram sitting at the top of that list as the most-capped Frenchman of all time with his 142 appearances.
Henry, Marcel Desailly, Hugo Lloris, Zinedine Zidane, Patrick Vieira and Deschamps are the other players to have managed that feat.
Paris [France], October 8
Olivier Giroud became the second-highest scorer for France after netting a brace in the country's 7-1 triumph over Ukraine in a friendly clash at Stade de France on Wednesday.
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