The chemical transformation of ammonium cyanate into urea has been of interest to many generations of scientists since its discovery by Friedrich Wöhler in 1828. Although widely studied both experimentally and theoretically, several mechanistic aspects of this reaction remain to be understood. In this paper, we apply computational methods to investigate the behavior of ammonium cyanate in the solid state under high pressure, employing a theoretical approach based on the self-consistent-charges density-functional tight-binding method (SCC-DFTB). The ammonium cyanate crystal structure was relaxed under external pressure ranging from 0 to 700 GPa, leading to the identification of five structural phases. Significantly, the phase at highest pressure (above 535 GPa) corresponds to the formation of urea molecules. At ca. 25 GPa, there is a phase transition of ammonium cyanate (from tetragonal P4/nmm to monoclinic P21/m) involving a rearrangement of the ammonium cyanate molecules. This transformation is critical for the subsequent transformation to urea. The crystalline phase of urea obtained above 535 GPa also has P21/m symmetry (Z = 2). This polymorph of urea has never been reported previously. Comparisons to the known (tetragonal) polymorph of urea found experimentally at ambient pressure suggests that the new polymorph is more stable above ca. 8 GPa. Our computational studies show that the transformation of ammonium cyanate into urea is strongly exothermic (enthalpy change -170 kJ mol-1 per formula unit between 530 and 535 GPa). The proposed mechanism for this transformation involves the transfer of two hydrogen atoms of the ammonium cation toward nitrogen atoms of neighboring cyanate anions, and the remaining NH2 group creates a C-NH2 bond with the cyanate unit.