  In this paper we consider Witten's bosonic open string field theory in the
presence of a constant background of the second-rank antisymmetric tensor field
$B_{ij}$. We extend the operator formulation of Gross and Jevicki in this
situation and construct the overlap vertices explicitly. As a result we find a
noncommutative structure of the Moyal type only in the zero-mode sector, which
is consistent with the result of the correlation functions among vertex
operators in the world sheet formulation. Furthermore we find out a certain
unitary transformation of the string field which absorbs the Moyal type
noncommutative structure. It can be regarded as a microscopic origin of the
transformation between the gauge fields in commutative and noncommutative gauge
theories discussed by Seiberg and Witten.
