In the centralized context, global constraints have been essential for the advancement of constraint reasoning. In this paper we propose to include soft global constraints in distributed constraint optimization problems (DCOPs). Looking for efficiency, we study possible decompositions of global constraints, including the use of extra variables. We extend the distributed search algorithm BnB-ADOPT+ to support these representations of global constraints. In addi- tion, we explore the relation of global constraints with soft local consistency in DCOPs, in particular for the generalized soft arc consistency (GAC) level. We in- clude specific propagators for some well-known soft global constraints. Finally, we provide empirical results on several benchmarks.