The utilization of additive manufacturing (AM) to engineer the permittivity profile of dielectric resonator antennas (DRAs) is considered. For the first time, the capabilities of AM are exploited to create continuously swept permittivity profiles and applied to cylindrical DRAs. The spatial variant lattices (SVL) synthesis algorithm is implemented to create the desired permittivity profiles from a single material, and resulting geometries are manufactured using a high-permittivity material in a fused deposition modeling AM process. Three individual antennas for global navigation satellite system bands are designed and manufactured, two inhomogeneous DRAs with continuous permittivity profiles along the radial and vertical axis, and one homogeneous DRA for comparison. The manufactured antennas are characterized by impedance, realized gain, and axial ratio. Experimental results agree well with simulations and show increased impedance-, gain-, and axial-ratio bandwidths for both inhomogeneous antennas compared to the homogeneous one.