The Ghana international, 31, had spells with Premier League sides Everton, Chelsea and Newcastle.
BBC reports Atsu had been missing since the 6 February quake that caused the collapse of his apartment in Antakya, Hatay.
"There are no words to describe our sadness," tweeted his Turkish top-flight club Hatayspor.
"We will not forget you, Atsu. Peace be upon you, beautiful person."
In the aftermath of the quake, Hatayspor initially reported Atsu had been rescued "with injuries", but a day later that position changed.
His agent Nana Sechere, who has been in Hatay, confirmed the news on Saturday on Twitter, writing: "It is with the heaviest of hearts that I have to announce to all well wishers that sadly Christian Atsu's body was recovered this morning.
"My deepest condolences go to his family and loved ones. I would like to take this opportunity to thank everyone for their prayers and support."
The Ghana Football Association said Atsu's body was recovered on Saturday morning after "almost two weeks of emotional torture".
The Ghanaian foreign ministry added that Atsu's elder brother and twin sister were at the site when his body was recovered.
Atsu's body was flown back to Ghana on Saturday for burial.
The ministry said it sent "deepest condolences to the widow and family".
The earthquake and aftershocks in southern Turkey and northern Syria are known to have killed more than 40,000 people.