Henry's formulation of seawater intrusion in coastal aquifers consists of a fully coupled system of flow and transport equations with variable density. While the Henry problem often serves as a benchmark for numerical codes, the accuracy of the existing analytical solutions is hard to gauge. We use a perturbation expansion in a small parameter, the ratio between the densities of seawater and freshwater, to derive an analytical solution for the transient Henry problem, which describes the saline intrusion caused by a sudden change in fresh groundwater discharge. This approach is effective for other variable density flow scenario, since it allows one to decouple the flow and transport equations.