  The Noether Symmetry approach is applied to study an extended teleparallel
$f(T,\phi)$ gravity that contains the torsion scalar $T$ and the scalar field
$\phi$ in the context of an Friedmann-Lema\^{i}tre-Robertson-Walker space-time.
We investigate the Noether symmetry approach in $f(T,\phi)$ gravity formalism
with the specific form of $f(T,\phi)$ and analyze how to demonstrate a
nontrivial Noether vector. The Noether symmetry method is a helpful resource
for generating models and finding out the exact solution of the Lagrangian. In
this article, we go through how the Noether symmetry approach enables us to
define the form of the function $f(T,\phi)$ and obtain exact cosmological
solutions. We also find the analytical cosmological solutions to the field
equations, that is consistent with the Noether symmetry. Our results
demonstrate that the obtained solutions enable an accelerated expansion of the
Universe. We have also obtained the present value of the Hubble parameter,
deceleration parameter, and effective equation of state parameter, which is fit
in the range of current cosmological observations.
