Wenger revealed after Friday's win that Giroud, who has scored 97 goals in 231 appearances since joining from Montpellier in 2012, could have left the Gunners this summer.
The France worldwide came off the bench to head home in the 85th minute as the Gunners kicked off the Premier League season with a thrilling 4-3 win.
Arsenal looked a beaten team when Leicester led 3-2 early in the second half after Vardy grabbed his second goal before the substitutions gave them new vigour in attack.
Danny Welbeck then brought Arsenal back level on the brink of half-time.
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"I opened the door for him at some stage as it's important for him to play but I don't want him to go", Wenger said at the post-match news conference.
The France international's future had been in doubt following the club-record arrival of Alexandre Lacazette, with clubs both in England and back in his home country reportedly interested. "We love him and in the end he made a decision to stay". I keep the faith and I still believe I can have an important part to play this season in the club.
Wenger has always been desperate to keep Giroud because he offers something so different with his aerial presence but was also willing to let him leave if he felt that he needed a guarantee that he would start more regularly in this World Cup season. "We were quite good a year ago on corners and overall I believe that with a bit of work we can get that out of the system".
It's only the second time in eight seasons that Arsene Wenger's side have secured three points in their opening fixture.
"You come away from home, score three goals and are almost there and then concede two.bitterly disappointed", he said.
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Eddie Rosario , Byron Buxton and Joe Mauer all homered, and Joe drove in five runs for the first time since 2010. Miguel Cabrera came out of the game after he singled in the fifth inning, complaining of lower back stiffness.