  We derive the Hamiltonian for spherically symmetric Lovelock gravity using
the geometrodynamics approach pioneered by Kucha\v{r} in the context of
four-dimensional general relativity. When written in terms of the areal radius,
the generalized Misner-Sharp mass and their conjugate momenta, the generic
Lovelock action and Hamiltonian take on precisely the same simple forms as in
general relativity. This result supports the interpretation of Lovelock gravity
as the natural higher-dimensional extension of general relativity. It also
provides an important first step towards the study of the quantum mechanics,
Hamiltonian thermodynamics and formation of generic Lovelock black holes.
