Giroud replaces Michy Batshuayi at Stamford Bridge as a result of the Belgian's loan to Borussia Dortmund to fill the void left by Pierre-Emerick Aubameyang's move to Arsenal earlier in the day.
Brought in as support and competition for Alvaro Morata, he has signed an 18-month contract with Chelsea that will keep him at the club until the end of the 2018/19 season.
Although the number 12 shirt he wore at Arsenal and for France was available, Giroud has been assigned the number 18 shirt for the Blues.
"Chelsea is one of the biggest teams in the Premier League. 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 told Chelseafc.com.
Director Marina Granovskaia commented, "Olivier is a proven talent at the top level and we are very pleased to call him a Chelsea player.
"He has scored goals regularly throughout his career and is well accustomed to English football and the Premier League. We are sure he will be a fantastic signing."
Giroud leaves Arsenal after scoring 105 goals in just over 253 appearances since first joining the club in 2012. His best single season Premier League return to date came in the 2013/14 and 2015/16 campaigns when he found the net on 16 occasions.
In the latter season, he managed a total of 24 goals in all competitions.
Now 31 years of age, Giroud first rose to prominence during his time with Montpellier as the club from the south of France shocked Ligue 1 to claim an unlikely title in 2011/12.
It was only Giroud's second ever season of top flight football after starting out in the lower leagues, but he finished the campaign as the league's joint top scorer with 21 goals.