We propose a communication-driven mechanism for predicting triadic closure in complex networks. It is mathematically formulated on the basis of communicability distance functions that account for the quality of communication between nodes in the network. We study $25$ real-world networks and show that the proposed method predicts correctly $20\%$ of triadic closures in these networks, in contrast to the $7.6\%$ predicted by a random mechanism. We also show that the communication-driven method outperforms the random mechanism in explaining the clustering coefficient, average path length, and average communicability. The new method also displays some interesting features with regards to optimizing communication in networks.