A tandem magnetic refrigerator has been developed for continuous operation between 4.2 and 1.8 K. This paper presents the design, computer simulation and construction of the prototype machine. The- regenerative concept is employed in the magnetic refrigerator to obtain a cascaded magnetic Carnot cycle effect along the temperature axis from the cold end to the warm end. Entropy pumping action from the cold heat reservoir to the warm heat reservoir occurs in the active magnetic regenerator. The inherent sources of irreversibility in regenerative magnetic refrigerators, i.e. heat capacity imbalance between magnetic refrigerant and heat transport medium, helium entrainment and dead volume effect, have been minimized by design optimization of the system components. The magnetic system of the tandem refrigerator has two virtually identical units, each consisting of a gadolinium gallium garnet (GGG; Gd3Ga5O12) magnetic core, a superconducting magnet, a warm end heat exchanger and a cold end heat exchanger. These components are united by a cryogenic displacer which shuttles the heat transport medium, subatmospheric He-3 gas, between the two units. The prototype of the designed magnetic refrigerator has operated continuously, producing a net refrigeration rate of 12 mW per magnetic core at 1.8 K.