Depardieu reportedly has bought a house in Belgium and plans to seek citizenship there because of France's steep taxes.
Although the French Prime Minister Jean-Marc Ayrault publicly called the move "pathetic," Kadyrov said he is "ready to welcome the great artist" to his republic, Radio France Internationale reported.
France has a 75 percent tax rate for incomes more than 1 million euros ($1.3 million).
Depardieu, 63, defended his actions in an angry open letter to the prime minister published in the newspaper Journal du Dimanche.
"I'm leaving because you think success, creation, talent and anything different should be punished. I am sending you back my passport and social security, which I have never used," Depardieu wrote in the letter, adding the reasons behind his plan to leave France are "numerous and personal."
"I've no place to complain or to boast, but I refuse to be described as pathetic," he said.
The Wall Street Journal said Ayrault's office declined to comment on the letter.
Le Monde said Depardieu told friends Russian President Vladimir Putin had "already sent me a passport," but Putin's spokesman Dmitry Peskov later said the actor "most likely he was joking."
Depardieu is best known for his work in the films "Green Card" and "The Man in the Iron Mask." He plays a supporting role in the current release "Life of Pi."