Organolead trihalide perovskite materials have been successfully used as light absorbers in efficient photovoltaic cells. Two different cell structures, based on mesoscopic metal oxides and planar heterojunctions have already demonstrated very impressive advances in performance. Here, we report a bilayer architecture comprising the key features of mesoscopic and planar structures obtained by a fully solution-based process. We used CH3NH3 Pb(I(1-x)Br(x))3 (x = 0.1-0.15) as the absorbing layer and poly(triarylamine) as a hole-transporting material. The use of a mixed solvent of γ-butyrolactone and dimethylsulphoxide (DMSO) followed by toluene drop-casting leads to extremely uniform and dense perovskite layers via a CH3NH3I-PbI2-DMSO intermediate phase, and enables the fabrication of remarkably improved solar cells with a certified power-conversion efficiency of 16.2% and no hysteresis. These results provide important progress towards the understanding of the role of solution-processing in the realization of low-cost and highly efficient perovskite solar cells.