The photoevaporation of protoplanetary discs by nearby massive stars present in their birth cluster plays a vital role in their evolution. Previous modelling assumes that the disc behaves like a classical Keplerian accretion disc out to a radius where the photoevaporative outflow is launched. There is then an abrupt change in the angular velocity profile, and the outflow is modelled by forcing the fluid parcels to conserve their specific angular momenta. Instead, we model externally photoevaporating discs using the slim disc formalism. The slim disc approach self-consistently includes the advection of radial and angular momentum as well as angular momentum redistribution by internal viscous torques. Our resulting models produce a smooth transition from a rotationally supported Keplerian disc to a photoevaporative driven outflow, where this transition typically occurs over ∼4–5 scale heights. The penetration of ultraviolet photons predominately sets the radius of the transition and the viscosity’s strength plays a minor role. By studying the entrainment of dust particles in the outflow, we find a rapid change in the dust size and surface density distribution in the transition region due to the steep gas density gradients present. This rapid change in the dust properties leaves a potentially observable signature in the continuum spectral index of the disc at mm wavelengths. Using the slim disc formalism in future evolutionary calculations will reveal how both the gas and dust evolve in their outer regions and the observable imprints of the external photoevaporation process.