The Saturn-mass exoplanet WASP-39b has been the subject of extensive efforts to determine its atmospheric properties using transmission spectroscopy1,2,3,4. However, these efforts have been hampered by modelling degeneracies between composition and cloud properties that are caused by limited data quality5,6,7,8,9. Here we present the transmission spectrum of WASP-39b obtained using the Single-Object Slitless Spectroscopy (SOSS) mode of the Near Infrared Imager and Slitless Spectrograph (NIRISS) instrument on the JWST. This spectrum spans 0.6–2.8 μm in wavelength and shows several water-absorption bands, the potassium resonance doublet and signatures of clouds. The precision and broad wavelength coverage of NIRISS/SOSS allows us to break model degeneracies between cloud properties and the atmospheric composition of WASP-39b, favouring a heavy-element enhancement (‘metallicity’) of about 10–30 times the solar value, a sub-solar carbon-to-oxygen (C/O) ratio and a solar-to-super-solar potassium-to-oxygen (K/O) ratio. The observations are also best explained by wavelength-dependent, non-grey clouds with inhomogeneous coverageof the planet’s terminator.