  We compute the partition function of $2D$ Jackiw-Teitelboim (JT) gravity at
finite cutoff in two ways: (i) via an exact evaluation of the Wheeler-DeWitt
wave-functional in radial quantization and (ii) through a direct computation of
the Euclidean path integral. Both methods deal with Dirichlet boundary
conditions for the metric and the dilaton. In the first approach, the radial
wavefunctionals are found by reducing the constraint equations to two first
order functional derivative equations that can be solved exactly, including
factor ordering. In the second approach we perform the path integral exactly
when summing over surfaces with disk topology, to all orders in perturbation
theory in the cutoff. Both results precisely match the recently derived
partition function in the Schwarzian theory deformed by an operator analogous
to the $T\bar{T}$ deformation in $2D$ CFTs. This equality can be seen as
concrete evidence for the proposed holographic interpretation of the $T\bar{T}$
deformation as the movement of the AdS boundary to a finite radial distance in
the bulk.
