One of the challenges of neuromorphic computing is efficiently routing spikes from neurons to their connected synapses. The aim of this thesis is to design a spike-routing architecture for flexible connections on single-chip neuromorphic systems. A model for estimating area, power consumption, memory, spike latency and link utilisation for neuromorphic spike-routing architecture is described. This model leads to the proposal for a new spike-routing architecture with a hybrid addressing scheme and a novel synaptic encoding scheme. The proposed architecture is implemented in a SystemC simulation tool with a supporting tool for encoding arbitrary SNN topologies for the synapse encoding scheme. Running the simulations with synthetic benchmarks and a handwriting recognition SNN shows that the proposed architecture is memory-efficient and provides low latency spike-routing with high synaptic activation concurrency.