Giroud headed the winning goal for Antonio Conte's side as they remained in contention for a Champions League place by beating Liverpool 1-0.
Elsewhere in London, Wenger bid farewell to the Arsenal fans as his 22-year reign at the club reaches its end. The 5-0 win against Burnley was his last game at the Emirates, with only two away matches remaining.
Wenger signed Giroud from Montpellier in 2012 and the Frenchman went on to score 105 goals for Arsenal in over 250 games at the club, winning three FA Cups along the way.
"Everyone knows how much I owe him for having given me the opportunity to fulfil my childhood dream," Giroud said, quoted by ESPN. "It wasn't all easy, but he was always there and he has always supported me.
"At the end, we were a bit disappointed to be leaving one another, but it was just the way life wants it to be."
Giroud left Arsenal to join Chelsea in January but made it clear that he still holds Wenger in the highest regard.
"It's bizarre to not see him at Arsenal anymore, but I think he'll go somewhere else, because he wants to continue," Giroud added. "I have a lot of respect for what he has contributed to Arsenal, and he's going to leave a huge void behind him. It's the end of an era."
The win over Burnley was Wenger's 414th Premier League home game, more than any other manager. His final match will be next Sunday's visit to Huddersfield.