We demonstrate 5 dB net gain in an erbium-doped tellurium-oxide-coated silicon nitride waveguide. The amplifier design leverages the high refractive index and high gain in erbium-doped tellurite glass as well as the ultra-low losses and mature, reliable, and low-cost fabrication methods of silicon nitride waveguide technology. We show that the waveguide platform demonstrates low background propagation losses of 0.25 dB/cm based on a ring resonator device with a Q factor of 1.3×106 at 1640 nm. We measure 5 dB peak net gain at 1558 nm and >3dB of net gain across the C band in a 6.7 cm long waveguide for 35 mW of launched 1470 nm pump power. Gain per unit length of 1.7 and 1.4 dB/cm is measured in a 2.2 cm long waveguide for 970 and 1470 nm pump wavelengths, respectively. Amplifier simulations predict that >10dB gain can be achieved across the C band simply by optimizing waveguide length and fiber-chip coupling. These results demonstrate a promising approach for the monolithic integration of compact erbium-doped waveguide amplifiers on silicon nitride chips and within silicon-based photonic integrated circuits.