The lead-free halide double perovskite class of materials offers a promising venue for resolving issues related to toxicity of Pb and long-term stability of the lead-containing halide perovskites. We present a first-principles study of the lattice vibrations in Cs_{2}AgBiBr_{6}, the prototypical compound in this class and show that the lattice dynamics of Cs_{2}AgBiBr_{6} is highly anharmonic, largely in regards to tilting of AgBr_{6} and BiBr_{6} octahedra. Using an energy- and temperature-dependent phonon spectral function, we then show how the experimentally observed cubic-to-tetragonal phase transformation is caused by the collapse of a soft phonon branch. We finally reveal that the softness and anharmonicity of Cs_{2}AgBiBr_{6} yield an ultralow thermal conductivity, unexpected of high-symmetry cubic structures.