The England star has been impressed by the Frenchman's response to his club's pursuit of the Liverpool striker and believes he is now firmly established at the Emirates Stadium
Both goals in a 2-0 win over Southampton took the striker to 10 goals in all competitions this term as the Gunners increased their lead at the top of the Premier League table to four points.
And Wilshere feels the threat of Giroud potentially losing his place has motivated the former Montpellier man into producing his best form after a difficult first season.
"Olivier has been really impressive, especially at the beginning of the season when everyone was saying that Suarez was coming in to take his place," Wilshere told reporters.
"For someone playing in that position it would have been tough for him to lose his place, but he has shown great character and for me he's been our best player this season.
"He holds the ball up and brings others into play. He has learned that side of the game that the Premier League is tough and sometimes you have to push defenders off the ball.
"He works so hard, he has played nearly every game, but fair play to him because he keeps going and going. He has got a great physique and a great base of fitness. Hopefully he can continue that form."