A laserwire transverse electron beam size measurement system has been developed and operated at the Accelerator Test Facility 2 (ATF2) at KEK. Special electron beam optics were developed to create an approximately 1 x 100 {\mu}m (vertical x horizontal) electron beam at the laserwire location, which was profiled using a 150 mJ, 71 ps laser pulse with a wavelength of 532 nm. The precise characterisation of the laser propagation allows the non-Gaussian transverse profiles of the electron beam caused by the laser divergence to be deconvolved. A minimum vertical electron beam size of 1.07 ${\pm}$ 0.06 (stat.) ${\pm}$ 0.05 (sys.) {\mu}m was measured. A vertically focussing quadrupole just before the laserwire was varied whilst making laserwire measurements and the projected vertical emittance was measured to be 82.56 ${\pm}$ 3.04 pm rad.