In this article, we establish a connection between the mechanics of genome evolution and the topology of gene regulation networks, focusing in particular on the evolution of the feed-forward loop (FFL) circuits. For this, we design a model of stochastic duplications, deletions, and mutations of binding sites and genes and compare our results with yeast network data. We show that the mechanics of genome evolution may provide a mechanism of FFL circuit generation. Our simulations result in overrepresentation of FFL circuits as well as in their clustering around few regulator pairs, in concordance with data from transcription networks. The mechanism here proposed and the analysis of the yeast data show that regulator duplication could have played an important role in FFL evolution.