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Preceding vehicles typically dominate the movement of following vehicles in traffic systems, thereby significantly influencing the efficacy of eco-driving control that concentrates on vehicle speed optimization. To potentially mitigate the negative effect of preceding vehicles on eco-driving control at the signalized intersection, this study proposes an overtaking-enabled eco-approach control (OEAC) strategy. It combines driving lane planning and speed optimization for connected and automated vehicles to relax the first-in-first-out queuing policy at the signalized intersection, minimizing the host vehicle’s energy consumption and travel delay. The OEAC adopts a two-stage receding horizon control framework to derive optimal driving trajectories for adapting to dynamic traffic conditions. In the first stage, the driving lane optimization problem is formulated as a Markov decision process and solved using dynamic programming, which takes into account the uncertain disturbance from preceding vehicles. In the second stage, the vehicle’s speed trajectory with the minimal driving cost is optimized rapidly using Pontryagin’s minimum principle to obtain the closed-form analytical optimal solution. Extensive simulations are conducted to evaluate the effectiveness of the OEAC. The results show that the OEAC is excellent in driving cost reduction over constant speed and regular eco-approach and departure strategies in various traffic scenarios, with an average improvement of 20.91% and 5.62%, respectively.