The 31-year-old striker has agreed a one-and-a-half-year deal at Stamford Bridge and moves for an undisclosed fee.
"It’s a massive club and I am proud to sign for Chelsea, and I’m looking forward to playing," Giroud told Chelsea's official website. He will wear the No 18 shirt.
Giroud scored 73 Premier League goals in 180 appearances for Arsenal after joining from Montpellier in 2012.
The Frenchman is perhaps best remembered for his scorpion kick goal against Crystal Palace last season.
He is Chelsea’s third signing of the January transfer window after Ross Barkley and Emerson Palmieri.
He could make his Chelsea debut at Watford on Monday 5 February.
Chelsea also announced that forward Michy Batshuayi has joined Borussia Dortmund on loan until the end of the season.