The striker's switch was confirmed on Wednesday, with the 31-year-old penning an 18 month deal with his new club.
"Chelsea is one of the biggest teams in the Premier League," Giroud said in the club release. "They have won maybe the most trophies in the last six or seven years. It's a massive club and I am proud to sign for Chelsea, and I'm looking forward to playing."
The transfer brings an end to Giroud's five-and-a-half-year stay at Arsenal, having signed from Montpellier in 2012. During his time at the Emirates Stadium, the forward won three FA Cups.
Gunners boss Arsene Wenger paid tribute to Giroud following his final appearance for Arsenal, against Swansea on Tuesday.
"He is a guy who gave great service to the club, he never let us down on the commitment front and he saved us many times," Wenger said.
"I have personally, of course, taken him from Montpellier and he became a strong, regular international player for France and we have gone together through good and bad. But always I believe his behaviour has been top, top class and the respect is more linked to that than to all the rest."
Throughout his stint at Arsenal, the focus from supporters was often on Giroud's limitations. The Frenchman isn't the quickest across the ground, nor is he the most skilful with the ball at this feet. It means a specific type of football is needed to get the best from him.
It's why, perhaps, he saw his role diminish last term, with Alexis Sanchez used as a centre-forward. With Pierre-Emerick Aubameyang joining Arsenal after Sanchez's departure, Giroud has sought a new challenge with Chelsea.
Chelsea are getting a fine forward, too. The Frenchman is outstanding with his back to goal, able to hold the ball up, bring team-mates into the game and bully opposition defenders. He's capable of spectacular moments, too, as evidenced by his scorpion-kick finish against Crystal Palace in the Premier League last season.
His main strength is his aerial power in the penalty area, and as noted by OptaJoe, he is also renowned for making a big impression from the bench:
It's the type of forward Chelsea manager Antonio Conte has been chasing, and he'll be delighted to have secured a proven alternative to Alvaro Morata, who has struggled at times this term after a blistering start.
Of course, Chelsea will need to play to the forward's strengths, and in many ways having a relatively static centre-forward can make attacking play a little one-dimensional.
But Giroud is a goalscorer at the highest level and has shown consistently down the years for Arsenal he's adept at making a difference in big moments. He'll be hoping to enhance his reputation further at the Gunners' London rivals.