The ability of neural networks to associate successive states of network activity lies at the basis of many cognitive functions. Hence, we hypothesized that many ubiquitous structural and dynamical properties of local cortical networks result from associative learning. To test this hypothesis, we trained recurrent networks of excitatory and inhibitory neurons on memory sequences of varying lengths and compared network properties to those observed experimentally. We show that when the network is robustly loaded with near-maximum amount of associations it can support, it develops properties that are consistent with the observed probabilities of excitatory and inhibitory connections, shapes of connection weight distributions, overrepresentations of specific 3-neuron motifs, distributions of connection numbers in clusters of 3-8 neurons, sustained, irregular, and asynchronous firing activity, and balance of excitation and inhibition. What is more, memories loaded into the network can be retrieved even in the presence of noise comparable to the baseline variations in the postsynaptic potential. Confluence of these results suggests that many structural and dynamical properties of local cortical networks are simply a byproduct of associative learning.