  We consider a very general dilaton-axion system coupled to Einstein-Hilbert
gravity in arbitrary dimension and we carry out holographic renormalization for
any dimension up to and including five dimensions. This is achieved by
developing a new systematic algorithm for iteratively solving the radial
Hamilton-Jacobi equation in a derivative expansion. The boundary term derived
is valid not only for asymptotically AdS backgrounds, but also for more general
asymptotics, including non-conformal branes and Improved Holographic QCD. In
the second half of the paper, we apply the general result to Improved
Holographic QCD with arbitrary dilaton potential. In particular, we derive the
generalized Fefferman-Graham asymptotic expansions and provide a proof of the
holographic Ward identities.
