Embodiments of a constructions system for constructing a structure atop a foundation are disclosed. In an embodiment, the construction system includes a rail assembly. The rail assembly is configured to be mounted to the foundation. In addition, the construction system includes a gantry movably disposed on the rail assembly. The gantry is configured to translate along a first axis relative to the rail assembly. Further, the construction system includes a printing assembly movably disposed on the gantry. The printing assembly is configured to translate along a second axis relative to the gantry. The second axis is orthogonal to the first axis. The printing assembly is configured to deposit vertically stacked layers of an extrudable building material onto a top surface of the foundation to construct a structure.