The numerical simulation of Biot’s model is of great interest since reliable numerical methods for solving poroelastic problems are needed for the accurate solution of multiphysics phenomena appearing in a great variety of fields. In recent years, significant effort has been focused on designing efficient iterative solution methods for these problems. There are mainly three different approaches: the fully implicit schemes, the iterative coupling methods and the explicit approach. An alternative to the fully implicit or monolithic methods is a classical approach that considers separate software modules for mechanics and flow calculations, implemented in both a sequential or iterative setting. In this way, the fully coupled system is broken into subproblems (flow and mechanics problems) that are solved one after the other. The fully explicit coupling approach is a very simple scheme which allows much flexibility in the implementation and has a lower computational cost. Due to its appealing advantages, intensive research is currently being carried out in this direction. Although their application is common in practice, there exist only a few works devoted to their theoretical analysis. In this work, we consider the so-called explicit fixed-stress split scheme, which consists of solving the flow problem first with time-lagging the displacement term, followed by the solution of the mechanics problem. To the best of our knowledge, we provide the first convergence analysis of the explicit fixed-stress split scheme for Biot's equations. In particular, we prove that this algorithm is optimally convergent if the considered finite element discretization satisfies an inf-sup condition. In addition, with the aim of designing the simplest scheme for solving Biot's model, we also propose a similar decoupled algorithm for piecewise linear finite elements for both variables which arises from the novel stabilization recently proposed by the authors, and is demonstrated to be optimally convergent.