Every subarrangement of Weyl arrangements of type $ B_{\ell} $ is represented by a signed graph. Edelman and Reiner characterized freeness of subarrangements between type $ A_{\ell-1} $ and type $ B_{\ell} $ in terms of graphs. Recently, Suyama and the authors characterized freeness for subarrangements containing Boolean arrangements satisfying a certain condition. This article is a sequel to the previous work. Namely, we give a complete characterization for freeness of arrangements between Boolean arrangements and Weyl arrangements of type $ B_{\ell} $ in terms of graphs.