  We identify an eikonal regime in celestial CFT$_2$ in which massless 2-2
scattering is dominated by t-channel exchange. We derive a formula for the
celestial amplitude that resums exchanges of arbitrary integer spin to all
orders in the coupling. The resulting eikonal phase takes the same form as in
flat space with the powers of center-of-mass energy replaced by weight-shifting
operators on the celestial sphere. We independently compute the celestial
two-point function for a scalar propagating in a shockwave background and show
that to leading order in the gravitational coupling and for a suitable choice
of the source, the result agrees with the prediction from the celestial eikonal
formula for graviton exchange. We demonstrate that this two-point function can
be directly obtained from the corresponding formula in AdS$_4$ in a flat space
limit. We finally establish a general relation between scalar celestial
amplitudes in celestial CFT$_{d-1}$ and the flat space limit of scalar
AdS$_{d+1}$ Witten diagrams.
