A nanoprocessor constructed from intrinsically nanometre-scale building blocks is an essential component for controlling memory, nanosensors and other functions proposed for nanosystems assembled from the bottom up1,2,3. Important steps towards this goal over the past fifteen years include the realization of simple logic gates with individually assembled semiconductor nanowires and carbon nanotubes1,4,5,6,7,8, but with only 16 devices or fewer and a single function for each circuit. Recently, logic circuits also have been demonstrated that use two or three elements of a one-dimensional memristor array9, although such passive devices without gain are difficult to cascade. These circuits fall short of the requirements for a scalable, multifunctional nanoprocessor10,11 owing to challenges in materials, assembly and architecture on the nanoscale. Here we describe the design, fabrication and use of programmable and scalable logic tiles for nanoprocessors that surmount these hurdles. The tiles were built from programmable, non-volatile nanowire transistor arrays. Ge/Si core/shell nanowires12 coupled to designed dielectric shells yielded single-nanowire, non-volatile field-effect transistors (FETs) with uniform, programmable threshold voltages and the capability to drive cascaded elements. We developed an architecture to integrate the programmable nanowire FETs and define a logic tile consisting of two interconnected arrays with 496 functional configurable FET nodes in an area of ∼960 μm2. The logic tile was programmed and operated first as a full adder with a maximal voltage gain of ten and input–output voltage matching. Then we showed that the same logic tile can be reprogrammed and used to demonstrate full-subtractor, multiplexer, demultiplexer and clocked D-latch functions. These results represent a significant advance in the complexity and functionality of nanoelectronic circuits built from the bottom up with a tiled architecture that could be cascaded to realize fully integrated nanoprocessors with computing, memory and addressing capabilities.