Organometal halide perovskite semiconductors could potentially be used to realize field-effect transistors (FET) with high carrier mobilities. However, the performance of these transistors is currently limited by the migration of ionic surface defects. Here, we show that a surface cleaning and passivation technique, which is based on a sequence of three solution-based steps, can reduce the concentration of ionic surface defects in halide-based perovskites without perturbing the crystal lattice. The approach consists of an initial cleaning step using a polar/non-polar solvent, a healing step to remove surface organic halide vacancies, and a second cleaning step. The surface treatment is shown to restore clean, near hysteresis-free transistor operation even if the perovskite films are formed under non-optimized conditions and can improve room temperature FET mobility by two to three orders of magnitude compared to untreated films. Our methylammonium lead iodide (MAPbI3) FETs exhibit high n- and p-type mobilities of 3.0 cm2V-1s-1 and 1.8 cm2V-1s-1 respectively at 300 K, and higher values (9.2 cm2 V-1s-1; n-type) at 80 K. We also show that the approach can be used to transform PbI2 single crystals into high quality, two-dimensional perovskite single crystals.