In order to observe and quantify long-range neuronal connections in intact mouse brain by light microscopy, it is first necessary to clear the brain, thus suppressing refractive-index variations. Here we describe a method that clears the brain and preserves the signal from proteinaceous fluorophores using a pH-adjusted non-aqueous index-matching medium. Successful clearing is enabled through the use of either 1-propanol or tert-butanol during dehydration whilst maintaining a basic pH. We show that high-resolution fluorescence imaging of entire, structurally intact juvenile and adult mouse brains is possible at subcellular resolution, even following many months in clearing solution. We also show that axonal long-range projections that are EGFP-labelled by modified Rabies virus can be imaged throughout the brain using a purpose-built light-sheet fluorescence microscope. To demonstrate the viability of the technique, we determined a detailed map of the monosynaptic projections onto a target cell population in the lateral entorhinal cortex. This example demonstrates that our method permits the quantification of whole-brain connectivity patterns at the subcellular level in the uncut brain.