We consider optimization algorithms designed for variable horizon model predictive control. Traditionally, such problems are considered intractable for real-time applications that require fast computations, as they need to solve multiple optimal control problems with varying horizons at each sampling instance. The main contribution is an algorithm that efficiently solves multiple optimal control problems with different prediction horizons in a recursive manner. This algorithm has been successfully implemented and integrated into the OSQP solver, resulting in a real-time controller that is both fast and reliable. To assess the effectiveness of the approach, we conducted evaluations in both a realistic simulation environment and on real hardware during outdoor flight experiments. Specifically, we focused on two distinct rendezvous maneuvers for autonomous landings of unmanned aerial vehicles. The results obtained from these evaluations further validate the practicality and efficacy of the proposed algorithm.