  The $T\bar{T}$ deformed 2D CFTs correspond to AdS$_3$ gravity with Dirichlet
boundary condition at finite cutoff or equivalently a mixed boundary condition
at spatial infinity. In this work, we use the latter perspective and
Chern-Simons formalism of AdS$_3$ gravity to construct the surface charges and
associated algebra in $T\bar{T}$ deformed theories. Starting from the Ba\~nados
geometry, we obtain the Chern-Simons gauge fields for the $T\bar{T}$ deformed
geometry, which are parametrized by two independent charges. With help of the
mixed boundary condition, the residual gauge symmetries of the deformed gauge
fields and the associated surface charges were obtained respectively. The
charge algebra turns out to be a non-linear deformed Virasoro algebra, which
was obtained in different way by applying the cutoff perspective. Finally, we
propose a way to construct the time-independent charges from these surface
charges and they satisfy the field-dependent Virasoro algebra.
