  We show that quantum interference-based coherent control is a highly
efficient tool for tuning ultracold molecular collision dynamics, and is free
from the limitations of commonly used methods that rely on external
electromagnetic fields. By varying {the relative populations and} phases of an
initial coherent superpositions of degenerate molecular states, we demonstrate
complete coherent control over integral scattering cross sections in the
ultracold $s$-wave regime of both the initial and final collision channels. The
proposed control methodology is applied to ultracold O$_2$~+~O$_2$ collisions,
showing extensive control over $s$-wave spin-exchange cross sections and
product branching ratios over many orders of magnitude.
