The Material Plasma Exposure eXperiment (MPEX), which has completed its final design, is a new linear plasma device to advance the understanding of plasma-material interactions through the generation and delivery of plasmas as they are expected in future fusion reactor divertors. MPEX will be a steady-state device to study high-fluence exposures of plasma-facing materials and components. The requirements for the magnetic field at the heating stages and the target make the application of superconducting coils necessary. The final designs for the superconducting magnets have been developed using three cryostat designs with warm bore diameters of 65 cm and 156 cm. The large bores are required to for other systems such as vacuum, water cooling, and RF power. There are 19 superconducting coils in MPEX that are contained in six cryostats. Although design, fabrication, and testing for the magnets as stand-alone units are straightforward, challenges will arise during the integration of the system. Various field profiles will be used during operation. The magnetic field where the electron cyclotron heating occurs needs to operate at both 1.25 and 2.50 T. Analyses that have been performed on the final design include designing the coils and determining operating currents to meet field requirements, forces between cryostats, the effects of coil and/or cryostat movement, and quench analysis. To ensure that the magnetic field requirements are met, a plan for monitoring the magnetic field at specified locations has been developed which includes the effect of coil and/or cryostat movement.