Event cameras show great potential for visual odometry (VO) in handling challenging situations, such as fast motion and high dynamic range. Despite this promise, the sparse and motion-dependent characteristics of event data continue to limit the performance of feature-based or direct-based data association methods in practical applications. To address these limitations, we propose Deep Event Inertial Odometry (DEIO), the first monocular learning-based event-inertial framework, which combines a learning-based method with traditional nonlinear graph-based optimization. Specifically, an event-based recurrent network is adopted to provide accurate and sparse associations of event patches over time. DEIO further integrates it with the IMU to recover up-to-scale pose and provide robust state estimation. The Hessian information derived from the learned differentiable bundle adjustment (DBA) is utilized to optimize the co-visibility factor graph, which tightly incorporates event patch correspondences and IMU pre-integration within a keyframe-based sliding window. Comprehensive validations demonstrate that DEIO achieves superior performance on \textit{10} challenging public benchmarks compared with more than 20 state-of-the-art methods.