  We study tree-level celestial amplitudes in Yang-Mills theory -- Mellin
transforms of multi-gluon scattering amplitudes that convert them into the
correlators of conformal primary fields on two-dimensional celestial sphere. By
using purely field-theoretical methods, we show that the soft conformal limit
of celestial amplitudes, in which one of the primary field operators associated
to gauge bosons becomes a dimension one current, is dominated by the
contributions of low-energy soft particles. This result confirms conclusions
reached by using Yang-Mills theory formulated in curvilinear coordinates, as
pioneered by Strominger. By using well-known collinear limits of Yang-Mills
amplitudes, we derive the OPE rules for the primary fields and the holomorphic
currents arising in the conformally soft limit. The Ward identities following
from OPE have the same form as the identities derived by using soft theorems.
