Chelsea have announced the arrival of Arsenal striker Giroud on an 18-month contract for around £18 million (Dh93.5m) and Michy Batshuayi's departure for Borussia Dortmund in a loan deal until the end of the season.
Giroud, 31, who has struggled to hold down a regular starting spot since joining Arsenal in 2012, said he was delighted to be joining their London rivals.
The deals ended a merry-go-round of strikers between the clubs with Dortmund selling Pierre-Emerick Aubameyang to Arsenal earlier on Wednesday.
"Chelsea is one of the biggest teams in the Premier League," Giroud told Chelsea's official site. "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."
France international Giroud, 31, leaves Arsenal having scored 105 goals in 253 games since signing from Montpellier for a reported £12m in June 2012.
"Oli 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," Arsenal manager Arsene Wenger told the club's website.
"We signed 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 that his behaviour has been top, top class.
"He always had his heart 100 per cent in the team and he was committed."
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Chelsea manager Antonio Conte had been linked with several strikers, including West Ham United's Andy Carroll, but finally moved for Giroud.
It allowed Batshuayi, who joined for a reported £33m from Marseille in 2016, to leave on loan with the forward having struggled to make a consistent impact at Stamford Bridge.
He has made 53 appearances for the club, scoring 19 times, and netted the goal in the 1-0 win at West Bromwich Albion in 2017 which clinched the Premier League title.
"In order to achieve my big objective, I want to play as much as possible and score many goals," he told Dortmund's official site. "The World Cup is taking place in the summer."
Dortmund's sporting director Michael Zorc added: "Michy is a young, very interesting striker who boasts a good goalscoring record and has shown his extraordinary quality at Chelsea and Olympique Marseille, in the Belgian league and while playing for the national team."