In recent years, there has been ongoing effort in achieving efficient transport of excitons in monolayer transition metal dichalcogenides subjected to highly non-uniform strain. Here we investigate the transport of excitons and trions in monolayer semiconductor WS2 subjected to controlled non-uniform mechanical strain. An atomic force microscope (AFM)-based setup is applied to actively control and tune the strain profiles by indenting the monolayer with an AFM tip. Optical spectroscopy is used to reveal the dynamics of the excited carriers. The non-uniform strain configuration locally changes the valence and conduction bands of WS2, giving rise to effective forces attracting excitons and trions towards the point of maximum strain underneath the AFM tip. We observe large changes in the photoluminescence spectra of WS2 under strain, which we interpret using a drift–diffusion model. We show that the transport of neutral excitons, a process that was previously thought to be efficient in non-uniformly strained two-dimensional semiconductors and termed as funnelling, is negligible at room temperature, in contrast to previous observations. Conversely, we discover that redistribution of free carriers under non-uniform strain profiles leads to highly efficient conversion of excitons to trions. Conversion efficiency reaches up to about 100% even without electrical gating. Our results explain inconsistencies in previous experiments and pave the way towards new types of optoelectronic devices.