The propagation and controlled manipulation of strongly nonlinear, two-dimensional solitonic states in a thin, anisotropic ferromagnet are theoretically demonstrated. It has been recently proposed that spin-polarized currents in a nanocontact device could be used to nucleate a stationary dissipative droplet soliton. Here, an external magnetic field is introduced to accelerate and control the propagation of the soliton in a lossy medium. Soliton perturbation theory corroborated by two-dimensional micromagnetic simulations predicts several intriguing physical effects, including the acceleration of a stationary soliton by a magnetic field gradient, the stabilization of a stationary droplet by a uniform control field in the absence of spin torque, and the ability to control the soliton's speed by use of a time-varying, spatially uniform external field. Soliton propagation distances approach 10 µm in low loss media, suggesting that droplet solitons could be viable information carriers in future spintronic applications, analogous to optical solitons in fiber optic communications.