The BBC Radio Leeds cricket commentator, 63, was taken ill on Friday night and died last evening.
His passing leaves a huge hole in the cricketing fraternity, where he was an enormously popular and respected figure.
Yorkshire CCC chief executive Mark Arthur described him as “a very special person” and said: “He will be missed by everyone associated with Yorkshire cricket. Our thoughts are with his wife, Pat, and his family.”
Yorkshire chairman Steve Denison called him “one of the finest, most generous men I’ve had the privilege to meet”.
Former England batsman Alec Stewart tweeted that Mr Callaghan was “a top bloke who loved his cricket”, while former Yorkshire and England pace bowler Ryan Sidebottom said he was “the nicest man I’ve ever had the privilege to meet”. Yorkshire pace bowler Jack Brooks tweeted that he was a “consummate professional” and said it was “a privilege to have known him”.
Mr Callaghan, a former BBC Radio Leeds sports editor, also spent several years working in the rugby world.