Thermal rectification is a direction-dependent asymmetric heat transport phenomenon. Here we report the tunable solid-state thermal rectification by asymmetric nonlinear far-field radiation. The asymmetry in thermal conductivity and emissivity of a three-terminal device is realized by sputtering a thin metal film (radiation barrier: niobium, copper, or silver) on the top right half of a polyethylene terephthalate strip (emitter). Both the experiment and finite element analysis are in excellent agreement, revealing a thermal rectification ratio (TR) of 13.0% for the niobium-deposited specimen. The simulation demonstrates that the TR can be further increased to 74.5% by tuning asymmetry in thermal conductivity, emissivity, and surface area. The rectification can also be actively controlled, by gating the environmental temperature, resulting in a maximum TR of 93.1%. This work is applicable for a wide range of temperatures and device sizes, which may find applications in on-demand heat control and thermal logic gates.