Wind power uncertainty poses significant challenges for automatic generation control (AGC) systems. It can enhance control performances to explicitly consider wind power uncertainty distributions within controller design. However, widely accepted wind uncertainties usually follow non-Gaussian distributions, which may lead to complicated stochastic AGC modeling and high computational burdens. To overcome the issue, this paper presents a novel Itô-theory-based model for the stochastic control problem (SCP) of AGC systems, which reduces the computational burden of optimization considering non-Gaussian wind power uncertainty to the same scale as that for deterministic control problems. We present an Itô process model to exactly describe non-Gaussian wind power uncertainty, and then propose an SCP based on the concept of stochastic assessment functions (SAFs). Based on a convergent series expansion of the SAF, the SCP is reformulated as a certain deterministic control problem without sacrificing performance under non-Gaussian wind power uncertainty. The reformulated control problem is proven as a convex optimization, which can be solved efficiently. A case study demonstrates the efficiency and accuracy of the proposed approach compared with several conventional approaches.