Giroud's arrives at Stamford Bridge after struggling to cement a place in the Arsenal starting lineup this season, with manager Arsene Wenger preferring to start Frenchman Alexandre Lacazette as a lone striker.
Giroud provides Chelsea boss Antonio Conte with options up front and eases the pressure on their record signing Alvaro Morata, who has gone off the boil after a good start to life in London.
"Chelsea is one of the biggest teams in the Premier League," the 31-year-old Giroud said in a statement.
"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."
Giroud has made 16 league appearances this season, 15 as a substitute. He joined Arsenal from French side Montpellier in 2012 and his goal tally has hit double figures in each of the last five seasons.
Chelsea were linked with several strikers who could offer an aerial threat, including AS Roma's Edin Dzeko, Peter Crouch of Stoke City and Tottenham Hotspur's Fernando Llorente, before landing Giroud following Pierre-Emerick Aubameyang's arrival at Arsenal from Borussia Dortmund.
Chelsea's Belgian striker Michy Batshuayi has completed a loan move to Dortmund until the end of the season.
(Reporting by Hardik Vyas in Bengaluru,; editing by Ed Osmond)
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