The Blues said they exercised Giroud's option in April. The news comes following recent reports that the Frenchman would join AC Milan on a free transfer.
The club also announced it picked up Silva's option after winning last week's Champions League final. The Brazilian signed a one-year deal as a free agent last summer.
Giroud scored four goals against Sevilla in the Champions League group stage, and his stunning overhead kick against Atletico Madrid in the round of 16 was nominated as one of the best goals of the European campaign.
Chelsea could allow the 34-year-old to leave if a suitable offer arrives, according to The Telegraph's Matt Law. Milan are considered one of a number of clubs interested in signing the experienced striker.
Silva's extension wasn't as much of a surprise. The 36-year-old, who arrived on a free transfer from Paris Saint-Germain, scored twice in his debut season, but injuries limited his time on the pitch in the second half of the campaign.
"When we brought Thiago Silva in last summer, we knew we were adding a world-class player to the squad," club director Marina Granovskaia said. "Thiago has duly shown everyone at Chelsea his immense quality throughout this season, and he has had a huge influence on and off the pitch for us."
Chelsea also rewarded manager Thomas Tuchel on Friday with a new contract until June 2024.