For a compact Hausdorff space \(X\) and some functional space \(F(X)\) on \(X\) a weighted composition operator is defined as \(uC_ \varphi f(x):=u(x)f(\varphi (x))\), where \(\varphi: X\to X\) is an automorphism. The author obtains criteria for the operator \(uC_ \varphi: C(X)\to C(X)\) to be a Fredholm operator and finds that in the case when \(X\) is a regular space like an interval or a ball in \(\mathbb{R}^ n\) the condition is equivalent to the invertibility of \(uC_ \varphi\). An analogous result is obtained for weighted composition operators on \(L^ p(\mu)\) space with nonatomic measure \(\mu\).