The lungs are among the most deformable body organs, a mechanical feature that is key to the vital process of breathing. Current micromechanical constitutive models of the lung parenchyma construct the tissue response function either as strain-driven or pressure-driven. However, the lung parenchyma resembles an open-cell foam material consisting of a solid phase and a fluid phase that closely interact with each other. In this work, we introduce a novel finite-deformation micromechanical poroelastic model of the lung parenchyma. Using a two-scale homogenization framework for poroelasticity, we construct the effective coarse-scale response of the tissue by solving a poroelastic fine-scale problem. To this end, we develop a non-linear structural model based on a tetrakaidecahedron (TKD) unit cell that only depends on four microstructural parameters. We validate the TKD model showing that it predicts the effective response of representative volume elements (RVE) constructed from micro-computed-tomography images of the lung under several combinations of deformation and alveolar pressure. Further, we show that the estimation of the effective stress using the TKD model delivers a speed-up in computation time of more than 284,000 × when compared to RVE simulations, at the same time that it delivers higher numerical stability. In addition, we demonstrate through a sensitivity analysis that the model response predominantly depends on the alveolar-wall elasticity and initial tissue porosity, which are parameter values that are inherently connected to measurable microstructural features of the lung tissue. The present TKD model opens the door to large-scale poroelastic simulations of the lung by providing a predictive yet efficient constitutive model of the lung parenchyma. Codes are available for download at https://github.com/dehurtado/PoroelasticTKDModel.