The Blues exercised the clause last month as the France international was in the final year of his deal, meaning he would have become a free agent at the end of the currently suspended campaign.
Frank Lampard had previously discussed Chelsea's hopes of retaining both Giroud and Willian as their contracts ran down.
There was speculation they would be handed short-term deals permitted by the Premier League in order to allow them to complete the 2019-2020 season, if it were to run beyond June due to the coronavirus pandemic.
But, following the move confirmed on Wednesday, striker Giroud - who was heavily linked with a move to Inter - will be at Stamford Bridge next season as well.
"Since I have been back at Chelsea, Olivier has been brilliant as a professional and as a man in general," Lampard told Chelsea's official website on a day that also saw goalkeeper Willy Caballero sign an extension.
"He has great qualities to help the squad both on and off the pitch, not only with his talent but with the example he sets every day and the experience he brings to our young squad.
"I am very pleased that will continue next season."
Giroud, 33, had found starting opportunities hard to come by this season before growing in importance amid injury concerns for Tammy Abraham before the suspension of top-flight action.
He scored in the 4-0 home win over Everton, which was Chelsea's last outing before the shutdown, while he also struck in February's derby win over London rivals Tottenham.
"I am delighted to continue my journey and adventure at Chelsea," said Giroud, who arrived from Arsenal in January 2018.
"I can't wait to get back to playing and enjoying competitive football with my team-mates.
"I'm looking forward to wearing the Chelsea shirt again, especially in front of our fans at a full Stamford Bridge, whenever it is safe to do so."
Chelsea believe Giroud is an important presence as their young squad matures under Lampard.
Director Marina Granovskaia said: "His attitude when asked to play a supporting role has been exemplary.
"It is clear to the club that Olivier continues to be a player we want in the squad, especially as we maintain the important balance between top-quality experience and the exciting young talent we have available.
"He is a proven trophy winner who we hope can help our new generation to become that too."