Erbium-doped fibre lasers exhibit high coherence and low noise as required for fibre-optic sensing, gyroscopes, LiDAR and optical frequency metrology. Endowing erbium-based gain in photonic integrated circuits can provide a basis for miniaturizing low-noise fibre lasers to the chip-scale form factor and enable large-volume applications. Although major progress has been made on integrated lasers based on silicon photonics with III-V gain media, realizing low-noise integrated erbium-based lasers has, however, remained unachievable. Recent advances in photonic-integrated-circuit-based high-power erbium-doped amplifiers make a new class of rare-earth-ion-based lasers possible. Here we demonstrate a fully integrated erbium laser that achieves 50 Hz intrinsic linewidth, high output power up to 17 mW, low intensity noise and integration of a III-V pump laser, approaching the performance of fibre lasers and state-of-the-art semiconductor extended-cavity lasers. The laser circuit is based on an erbium-ion-implanted ultralow-loss silicon nitride photonic integrated circuit, with an intracavity microring-based Vernier filter that enables >40 nm wavelength tunability within the optical C and L bands and attains a 70 dB side-mode suppression ratio. This new class of low-noise, tunable integrated laser could find applications in LiDAR, microwave photonics, optical frequency synthesis and free-space communications, with wavelength extendibility using different rare-earth ion species.