Euler character of a numerically trivial divisor

Euler character of a numerically trivial divisor

Let $X$ be a projective variety and $D$ be a Cartier divisor on $X$.
Suppose $D$ is ${numerically}$ trivial, then is the Euler character
$\chi(X,D)= \chi(X, \mathcal{O}_X)$?
Here numerically trivial means the intersection number of the divisor $D$
with any curve is zero.
I saw somebody mentioned this result followed from Riemann-Roch, but did
not see the reason.