Psyche is a Discovery mission that will visit the asteroid (16) Psyche to determine if it is the metallic core of a once larger differentiated body or otherwise was formed from accretion of unmelted metal-rich material. The spacecraft will launch in August 2022 and arrive at the asteroid in January 2026. Psyche will carry three science instruments: a gamma ray and neutron spectrometer, a magnetometer, and a multispectral imager. Additionally, the spacecraft will host the Deep Space Optical Communications payload, which is a technology demonstration not required to meet Psyche's science objectives. The magnetometer is composed of two identical high-sensitivity magnetic field fluxgate sensors mounted in a gradiometer configuration that enables the rejection of meter-scale stray fields from the spacecraft. The instrument is key to meeting mission objectives since measurements of a strong asteroid remanent magnetic field will unambiguously indicate that (16) Psyche is an iron core. The magnetic signature from the spacecraft is the main source of noise for the magnetometer, both for DC and AC magnetic fields. Limiting and characterizing spacecraft-generated magnetic fields is therefore essential to the mission. This is the objective of the Psyche's magnetics control program described in this paper. The first step towards a successful program was to establish a set of magnetic cleanliness requirements directly derived from the magnetometer science performance and Psyche's range of expected fields. Test and modeling efforts of DC and AC fields of spacecraft components were then put in place to characterize and understand the spacecraft fields and enable verification of the cleanliness requirements. In this paper we describe the derivation of these requirements, test and analyses methods, and more generally the processes and procedures that govern the magnetics program for Psyche. The paper concludes with a discussion of the challenges and work to go and a comparison with the magnetic control processes of other missions with similar magnetic cleanliness constraints.