The Newcastle website gave no reason for the departure but quoted Llambias as saying he had been on "an incredible journey" during his five years at the club, "including some challenging times".
Llambias had said in a statement on Tuesday that "the board are pleased to welcome Joe back to the club".
Kinnear's appointment on a three-year deal has been criticised by some fans while manager Alan Pardew - who now reports to the director of football - has yet to comment publicly.
Former Newcastle manager Kinnear gave a bizarre radio interview on Monday, making a series of gaffes including mispronouncing Llambias's name along with those of some club players.
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