Additive manufacturing of high-entropy alloys combines the mechanical properties of this novel family of alloys with the geometrical freedom and complexity required by modern designs. Here, a non-beam approach to additive manufacturing of high-entropy alloys is developed based on 3D extrusion of inks containing a blend of oxide nanopowders (Co3O4 + Cr2O3 + Fe2O3 + NiO), followed by co-reduction to metals, inter-diffusion and sintering to near-full density CoCrFeNi in H2. A complex phase evolution path is observed by in-situ X-ray diffraction in extruded filaments when the oxide phases undergo reduction and the resulting metals inter-diffuse, ultimately forming face-centered-cubic equiatomic CoCrFeNi alloy. Linked to the phase evolution is a complex structural evolution, from loosely packed oxide particles in the green body to fully-annealed, metallic CoCrFeNi with 99.6 ± 0.1% relative density. CoCrFeNi micro-lattices are created with strut diameters as low as 100 μm and excellent mechanical properties at ambient and cryogenic temperatures.