Giroud's contract was set to expire in June 2018, while Koscielny and Coquelin were originally tied to the club for a further year, but all three have signed new "long-term contracts".
Manager Arsene Wenger said in a statement: "We are very pleased that three important members of our team have committed to us for the long term.
"Francis has made tremendous technical strides over the past few years because he's so focused every day.
"Olivier has big experience in the game now and has become a more and more complete player since joining us.
"Laurent is of course a key part of our squad and I believe one of the best defenders in the world today. So overall, this is great news for us."
Giroud's was Arsenal's highest-scoring player last season with 24 goals in all competitions and has struck nine times this term.
Koscielny, who revealed his new agreement runs until 2020 on Twitter, has made 273 appearances since arriving from Lorient in 2010, while Coquelin has made 131 senior outings for the club.
While Arsenal will be delighted to have agreed new contracts with the French trio, uncertainty still remains over the futures of Mesut Ozil and Alexis Sanchez.
Ozil and Sanchez's deal will expire at the end of next season, and Wenger will likely focus his attention on tying them down long term.