Automatic identification and tracking of mesoscale eddies are crucial in large oceanic observational and numerical model data. This work proposes a fully automated method that identifies and tracks from a single Lagrangian advection, all mesoscale eddies, without prior knowledge of their lifespans. The eddies' detection and tracking use a hybrid method based on geometrical properties of the evolving velocity along Lagrangian trajectories and a grid density-based clustering algorithm. The high eddies' monitoring capacity of the proposed method is demonstrated by automatically identifying and tracking these structures from two different datasets: satellite-derived surface geostrophic velocity fields and a two-dimensional fluid simulation. The proposed approach gives complete dynamical features and evolution of the detected mesoscale eddies by identifying their genesis event, monitoring their coherent core, and describing their splitting and vanishing image.