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In spite of clear fan‐shaped magnetic anomalies in the Eastern Algero‐Balearic Basin (EABB), the way how and the time when seafloor spreading occurred are still debated. In this work, a new seismo‐stratigraphic interpretation based on deep‐penetration reflection seismic data correlated to reduced‐to‐the‐pole magnetic anomalies and on‐offshore litho‐stratigraphic correlation of Pre‐Messinian units brings new constraints on its age and mode of opening. Our results reveal that the seafloor spreading of the EABB occurred at an intermediate half‐spreading rate of 3.7 ± 0.5 cm/yr for 2.45 ± 0.18 Myr during the Langhian‐Serravallian times, that is, after the Corsica‐Sardinia block rotation and the collision of Lesser Kabylia with Africa. We revise the kinematics of the Algero‐Balearic domain into three stages: (a) birth of a highly stretched continental basin accommodating the southern drift of the Kabylies driven by slab rollback between ∼23 and ∼15 Ma, (b) fast opening of a new EABB between 15.2 and 12.7 Ma by clockwise rotation of a Greater Alboran Block (GALB) promoted by slab tearing, and (c) late East‐West opening of the western basin in response to the westward retreat of the Gibraltar slab and westward slab tearing propagation and the concomitant migration of the GALB. The last stages match both the late formation of Subduction‐Transform Edge Propagator faults at the toes of the Algero‐Balearic margins and the post‐collisional volcanic migration along the Algerian margin interpreted as related to slab tearing propagation. This new scenario favors a significant stretching and splitting of the GALB into several continental fragments resulting from the westward propagation of the arcuate subduction front by lateral tearing of a narrow slab. Key Points: New seismo‐stratigraphic interpretation of the pre‐Messinian units and analysis of a reduced‐to‐the‐pole magnetic anomaly pattern of the Eastern Algero‐Balearic basinReassessment of previous kinematic reconstructions of the Algero‐Balearic basin evidencing the oceanic ridge migration during the Middle‐Late MioceneThe combination of the Tethyan slab rollback and slab tearing explains the fast rotation, translation, and fragmentation of the Greater Alboran block after the collision of the Kabylies [ABSTRACT FROM AUTHOR]