  In this paper we perform in a manifestly $SO(n-1,1)$ [or, alternatively
$SO(n)$] covariant fashion, the canonical analysis of general relativity in $n$
dimensions written as a constrained $BF$ theory. Since the Lagrangian action of
the theory can be written in two classically equivalent ways, we analyze each
case separately. We show that for either action the canonical analysis can be
accomplished without introducing second-class constraints during the whole
process. Furthermore, in each case the resulting Hamiltonian formulation is the
same as the canonical formulation with only first-class constraints recently
obtained in M. Montesinos, R. Escobedo, J. Romero, and M. Celada, Phys. Rev. D
101, 024042 (2020) from the $n$-dimensional Palatini action.
