MoS2 atomic layers have recently attracted much interest because of their two-dimensional structure as well as tunable optical, electrical, and mechanical properties for next generation electronic and electro-optical devices. Here we have achieved facile fabrication of MoS2 thin films on CdS nanowires by cation exchange in solution at room temperature and importantly observed their extraordinary magnetic properties. We establish the atomic structure of the MoS2/CdS heterostructure by taking atomic images of the MoS2/CdS interface as well as performing first-principles density functional geometry optimizations and STEM-ADF image simulations. Furthermore, our first principles density functional calculations for the MoS2/CdS heterostructure reveal that the magnetism in the MoS2/CdS heterostructure stems from the ferromagnetic MoS2 monolayer next to the MoS2/CdS interface. The ferromagnetism is attributed to the partial occupation of the Mo dx2-y2/dxy conduction band in the interfacial MoS2 monolayer caused by the mixed covalent-ionic bonding among the MoS2 and CdS monolayers near the MoS2/CdS interface. The present findings of the ferromagnetic MoS2 monolayer with large spin polarization at the MoS2-semiconductor interface suggest a new route for fabrication of the transition metal dichalcogenide-based magnetic semiconductor multilayers for applications in spintronic devices.