We give a method for deciding unifiability in the variety of bounded distributive lattices. For this, we reduce the problem of deciding whether a unification problem S has a solution to the problem of checking the satisfiability of a set Φ S of ground clauses. This is achieved by using a structure-preserving translation to clause form. The satisfiability check can then be performed by either a resolution-based theorem prover or a SAT checker. We apply the method to unification with free constants and to unification with linear constant restrictions, and show that, in fact, it yields a decision procedure for the positive theory of the variety of bounded distributive lattices. We also consider the problem of unification over (i.e., in an algebraic extension of) the free lattice. Complexity issues are also addressed.