An automatic machine for covering the covers of a book of different dimensions starting from a film sheet; the machine comprises a work plane in which the film sheet is arranged, means for welding and cutting the film sheet, first and second means for folding the ends of the film sheet and a control unit adapted to control the welding and cutting means and the first and second folding means as a function of the book dimension for covering the book covers. The machine comprises reception and gripping means configured to receive the book with the open covers at the input position and adapted to grip the body of the book outside the work plane and transport the book to the working position over the film sheet for the operation of covering the book covers.