An integrated rechargeable electrochemical cell, comprising: - a positive electrical current collector formed of a high thermal and electric conductivity material; - a negative electrical current collector formed of a high thermal and electric conductivity material; - a cathodic electrode formed of a conductive substrate, a polymeric binder, and a catalyst which during the charging step by means of an electrical current is capable of splitting the water molecules of the air conveyed internally thereto, thus obtaining oxygen, whereas in the discharging step it is capable of electrochemically reducing the oxygen of the air conveyed internally thereto; - an anodic electrode formed of a conductive substrate, a polymeric binder, and a catalyst, which during the charging step by means of an electrical current is capable of splitting the water molecules that electro-osmotically permeate from the cathode through a separator, thus obtaining hydrogen, whereas during the discharging step it is capable of electrochemically oxidizing the hydrogen present in the anodic compartment; - a gas-impermeable and electrically insulating separator, placed between said electrodes (3, 4) and formed of a polymeric membrane rich in ion exchange groups and capable of guaranteeing ionic conductivity; - an electrically conductive porous support, placed between said positive electrode and said positive current collector, performing the function of a gas diffusion layer; - an electrically conductive porous support, placed between said negative electrode and said negative current collector, containing powders of hydride metals capable of rapidly absorbing gaseous hydrogen (up to 2-3% by weight) and gradually releasing it; - an inlet channel suitable for conveying air into said porous support; - an outlet channel for extracting air from said porous support; said cathodic electrode and said porous support form a gas-impermeable and hermetically sealed cathodic compartment between the positive current collector and the separator, whereas said anodic electrode and said porous support form a gas-impermeable and hermetically sealed anodic compartment between the negative current collector and the separator, characterized in that the anodic compartment features an inlet channel through which it is possible to inject gaseous hydrogen directly into said porous support in which said hydrogen is adsorbed, said porous support having the same width and length as the anodic electrode but a thickness 20 to 30 times greater. - a positive electrical current collector formed of a high thermal and electric conductivity material; - a negative electrical current collector formed of a high thermal and electric conductivity material; - a cathodic electrode formed of a conductive substrate, a polymeric binder, and a catalyst which during the charging step by means of an electrical current is capable of splitting the water molecules of the air conveyed internally thereto, thus obtaining oxygen, whereas in the discharging step it is capable of electrochemically reducing the oxygen of the air conveyed internally thereto; - an anodic electrode formed of a conductive substrate, a polymeric binder, and a catalyst, which during the charging step by means of an electrical current is capable of splitting the water molecules that electro-osmotically permeate from the cathode through a separator, thus obtaining hydrogen, whereas during the discharging step it is capable of electrochemically oxidizing the hydrogen present in the anodic compartment; - a gas-impermeable and electrically insulating separator, placed between said electrodes (3, 4) and formed of a polymeric membrane rich in ion exchange groups and capable of guaranteeing ionic conductivity; - an electrically conductive porous support, placed between said positive electrode and said positive current collector, performing the function of a gas diffusion layer; - an electrically conductive porous support, placed between said negative electrode and said negative current collector, containing powders of hydride metals capable of rapidly absorbing gaseous hydrogen (up to 2-3% by weight) and gradually releasing it; - an inlet channel suitable for conveying air into said porous support; - an outlet channel for extracting air from said porous support; said cathodic electrode and said porous support form a gas-impermeable and hermetically sealed cathodic compartment between the positive current collector and the separator, whereas said anodic electrode and said porous support form a gas-impermeable and hermetically sealed anodic compartment between the negative current collector and the separator, characterized in that the anodic compartment features an inlet channel through which it is possible to inject gaseous hydrogen directly into said porous support in which said hydrogen is adsorbed, said porous support having the same width and length as the anodic electrode but a thickness 20 to 30 times greater.