The France international came off the bench to score the winner in the Gunners' 4-3 victory over Leicester City in the 2017-18 Premier League opener in North London.
Giroud only made the starting XI 11 times in the league last season, prompting rumours of the player pining for a move away in a bid to find first-team football.
Speaking after the seven-goal thriller at the Emirates, Wenger told Sky Sports News: "I love the man and the player. He's a fantastic guy and he's committed.
"He doesn't want to leave and I'm happy he wants to stay. At one stage I opened the door for him as I knew I had many strikers, and in the end he decided to stay."
Giroud has been at Arsenal since 2012, and in that time has scored 99 goals for the club.