Pierre-Emerick Aubameyang scored twice as the Gunners came from behind to beat Frank Lampard’s side and win the cup for a record 14th time.
Christian Pulisic had fired Chelsea ahead before Aubameyang equalised from the spot after Cesar Azpilicueta brought him down.
The Gabon international then hit the winner in the second half before Chelsea’s Mateo Kovacic was later sent off for two yellow card offences.
And taking to social media after the game, the forward screen shotted a congratulations message sent to him, which included a picture of a dejected looking Giroud, and added two dancing emojis.
Giroud ended his five-and-a-half year stay at Arsenal to join close rivals Chelsea in January 2018.
The French striker moved to Stamford Bridge in an £18million transfer on deadline day in 2018 after Pierre-Emerick Aubameyang joined the Gunners a club-record £56m fee.
Speaking on his decision to leave the Gunners, he told France Football at the time: “I went to see the coach to ask him where he was with Aubameyang.
“I put him under a bit of pressure, like my agent, who I spoke to several times a day. It is normal. I did not want to be deprived of going to Chelsea, which was the best solution for me.
“The coach immediately said to me: “Don’t worry, I will do my best so that you are happy”. On one side, it was normal. I had never asked to leave.”
Before he added: “It was frustrating at Arsenal obviously. For a year and a half, it went from bad to worse. I could no longer continue like that.
“I could not bring myself to spend another year at Arsenal and remain a reserve, even a second reserve. The future looked gloomy with the arrival of a new striker.”