  We present an analytical method for computing the mean cover time of a random
walk process on arbitrary, complex networks. The cover time is defined as the
time a random walker requires to visit every node in the network at least once.
This quantity is particularly important for random search processes and target
localization in network topologies. Based on the global mean first passage time
of target nodes we derive an estimate for the cumulative distribution function
of the cover time based on first passage time statistics. We show that our
result can be applied to various model networks, including Erd\H{o}s-R\'enyi
and Barab\'asi-Albert networks, as well as various real-world networks. Our
results reveal an intimate link between first passage and cover time statistics
in networks in which structurally induced temporal correlations decay quickly
and offer a computationally efficient way for estimating cover times in network
related applications.
