This paper introduces the Adaptive Elastic-net estimator for ergodic diffusion processes, demonstrating oracle properties in an asymptotic regime with mixed rates, crucial for such processes, ensuring consistent selection of relevant variables and optimal convergence rates. Additionally, it describes an iterative algorithm for parameter estimation, along with presenting the regularization path in a simulation study. This paper serves as a starting point for further investigation into various types of stochastic processes, offering potential improvements in prediction accuracy and interpretability.