The recently discovered nickelate superconductor La3Ni2O7 has a high transition temperature near 80 K under pressure, providing an additional avenue for exploring unconventional superconductivity. Here, with state-of-the-art tensor-network methods, we study a bilayer t-J-J⊥ model for La3Ni2O7 and find a robust s-wave superconductive (SC) order mediated by interlayer magnetic couplings. Large-scale density matrix renormalization group calculations find algebraic pairing correlations with Luttinger parameter Ksc ≲ 1. Infinite projected entangled-pair state method obtains a nonzero SC order directly in the thermodynamic limit, and estimates a strong pairing strength Δz ∼ O(0.1). Tangent-space tensor renormalization group simulations elucidate the temperature evolution of SC pairing and further determine a high SC temperature Tc*/J ∼ O(0.1). Because of the intriguing orbital selective behaviors and strong Hund’s rule coupling in the compound, t-J-J⊥ model has strong interlayer spin exchange (while negligible interlayer hopping), which greatly enhances the SC pairing in the bilayer system. Such a magnetically mediated pairing has also been observed recently in the optical lattice of ultracold atoms. Our accurate and comprehensive tensor-network calculations reveal a robust SC order in the bilayer t-J-J⊥ model and shed light on the pairing mechanism of the high-Tc nickelate superconductor.