We construct explicitly the canonical transformation which controls the full dependence (local and nonlocal) of the vertex functional of a Yang-Mills theory on a background field. After showing that the canonical transformation found is nothing but a direct field-theoretic generalization of the Lie transform of classical analytical mechanics, we comment on a number of possible applications, and, in particular, the nonperturbative implementation of the background field method on the lattice, the background field formulation of the two-particle irreducible formalism, and, finally, the formulation of the Schwinger-Dyson series in the presence of topologically nontrivial configurations.

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