A comprehensive study is made for the magnetic moments of octet baryons in the method of QCD sum rules. A complete set of QCD sum rules is derived using the external-field method and generalized interpolating fields. For each member, three sum rules are constructed from three independent tensor structures. They are analyzed in conjunction with the corresponding mass sum rules. The performance of each of the sum rules is examined using the criteria of operator product expansion convergence and ground-state dominance, along with the role of the transitions in intermediate states. Individual contributions from the $u$, $d$, and $s$ quarks are isolated and their implications in the underlying dynamics are explored. Valid sum rules are identified and their predictions are obtained. The results are compared with experiment and previous calculations.