Accies chairman Ronnie McDonald and vice-chairman Les Gray are to split the duties carried out by Paterson, who left New Douglas Park to concentrate on his business interests.
A statement from McDonald on Hamilton's official website said: "After several years sterling service as a director and chief executive, George Paterson has stepped down to devote more time to his business interests.
"George played a major part in the club securing it's UEFA club licence and representing the club at the SFL and SFA.
"We wish George every success in the future and I hope he will be back to enjoy many more 'Accies' fixtures in the future.
"We will not be appointing anyone to the vacant position, preferring to spread the duties between myself and Les Gray."