  Noncommutative gauge theories can be constructed from ordinary $U(\infty)$
gauge theories in lower dimensions. Using this construction we identify the
operators on noncommutative D-branes which couple to linearized supergravity
backgrounds, from a knowledge of such couplings to lower dimensional D-branes
with no $B$ field. These operators belong to a class of gauge invariant
observables involving open Wilson lines. Assuming a DBI form of the coupling we
show, to second order in the gauge potential but to all orders of the
noncommutativity parameter, that our proposal agrees with the operator obtained
in terms of ordinary gauge fields by considering brane actions in backgrounds
and then using the Seiberg-Witten map to rewrite this in terms of
noncommutative gauge fields. Our result clarify why a certain {\it commutative}
but {\it non-associative} ``generalized star product'' appears both in the
expansion of the open Wilson line, as well as in string amplitude computations
of open string - closed string couplings. We outline how our procedure can be
used to obtain operators in the noncommutative theory which are holographically
dual to supergravity modes.
