Centre-back Silva, who turns 36 next month, has been in talks with clubs including Chelsea and Fiorentina after deciding to leave Paris at the end of eight hugely successful seasons.
Choupo-Moting, whose winning goal sent PSG into the Champions League semi-finals at Atalanta's expense, is also leaving Parc des Princes after two years since his arrival from Stoke City.
Mbappe described Silva as a "legend" of the club and said Choupo-Moting had been "like a big brother" and under appreciated for his abilities.
Kylian Mbappé appears to announce the departures from PSG of Eric-Maxim Choupo-Moting & Thiago Silva via his Instagram story.— Get French Football News (@GFFN) August 26, 2020
In an Instagram story post on Wednesday, PSG forward Mbappe said: "This is the end. I'm very sad to say goodbye to you and that your adventure has come to an end, but I'm also very proud to have been able to play with you.
"Thiago Silva: captain, you're a legend, you have marked the history of this club. One of the best I've seen and have played with.
"Choupo-Moting: you were like a big brother for me for two years. It took a long time for people to realize what a great player you are. But, above all, you're a great guy.
"Thank you so much, guys, I will miss you."