The actor is welcome to join the company with a monthly salary of $755.
The theatre's manager said that Mr. Depardieu should expected an official invitation later this month.
Last week the actor received a Russian passport from President Vladimir Putin during their meeting in the Black Sea resort town of Sochi.
Depardieu made headlines after he fled his native France to avoid the 75 percent tax rate on income over 1 million euros.
Voice of Russia, Vesti.ru
French film star Gérard Depardieu failed to appear in court to face drunk-driving charges because he was in Montenegro preparing to play disgraced former IMF chief Dominique Strauss-Kahn in a film.
"Despite wanting to be there and meet the judges and in no way to escape justice, Gérard Depardieu absolutely could not be present," his lawyer told reporters outside the Paris courtroom.
The no-show on Tuesday means the case will turn into a full trial and a tougher sentence for the 64-year-old actor – a 4,500 euro fine and a possible two years in prison.
Depardieu is accused of crashing his scooter in Paris with more than three times the legal limit of alcohol in his blood. No one else was injured in the accident.
On Sunday he accepted a Russian passport. On Monday he denied he was leaving France for tax reasons, insisting he remained French.
Voice of Russia, Reuters
French actor Gerard Depardieu has met President Vladimir Putin and has been handed his new Russian passport.
The actor had announced he was seeking Russian citizenship after the French government criticized his decision to move abroad to avoid higher taxes.
Mr. Depardieu met Mr. Putin in Russia's Black Sea resort of Sochi.
Mr. Depardieu was then given his new passport, although the president's spokesman said Mr. Putin did not hand it over personally.
Mr. Depardieu and Mr. Putin shook hands and hugged each other at the meeting in Sochi.
Earlier this week, Mr. Putin signed the decree granting Russian citizenship to Mr. Depardieu.
The actor responded by writing an open letter saying: "I love your country, Russia - its people, its history, its writers. I love your culture, your intelligence."
Mr. Depardieu went on to describe Russia as "a great democracy, and not a country where the prime minister calls one of its citizens shabby".
Russian President Vladimir Putin has welcomed French actor Gerard Depardieu in the Black Sea resort city of Sochi to hand him a Russian passport, Putin`s spokesman Dmitry Peskov told the media.
He added that Mr. Depardieu has been visiting Russia ‘on a private trip’.
The actor announced he was seeking Russian citizenship after the French government criticized his decision to move abroad to avoid 75% taxes.
Depardieu did not change his mind even after the tax decision was cancelled.
Voice of Russia, RIA, BBC