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The France striker moved across London to join the Blues in an £18m transfer deadline day deal.
The 31-year-old signed an 18-month contract having been restricted to just one Premier League start at Arsenal this season.
Giroud netted 105 goals in 253 appearances during his Gunners career since joining for £12m in 2012.
And he took to social media to thank the fans for their support during his time at the Emirates.
“I spent five and a half amazing years within the Arsenal family,” he wrote on Twitter.
“This beautiful story ends today. Thank you for your warm welcome.
“I would like to especially thank the fans for their unconditional support upon my arrival.”
Antonio Conte’s search for a target man had seen Chelsea linked with at least half-a-dozen front men.
Former Montpellier star Giroud said on Twitter that he was eagerly anticipating making his first Stamford Bridge appearance.
But with his new club suffering a humiliating 3-0 home defeat by Bournemouth last night his debut may come sooner than expected.
“I’m delighted and proud to become a Chelsea player,” he wrote in a later post.
“Looking forward to make my debut. Come on the Blues! #TheBlues”