  We present a $D$-dimensional Bardeen like Anti-de Sitter (AdS) black hole
solution in Einstein-Gauss-Bonnet (EGB) gravity, \textit{viz}., Bardeen-EGB-AdS
black holes. The Bardeen-EGB-AdS black hole has an additional parameter due to
charge ($e$), apart from mass ($M$) and Gauss-Bonnet parameter ($\alpha$).
Interestingly, for each value of $\alpha$, there exist a critical $e = e_E$
which corresponds to an extremal regular black hole with degenerate horizons,
while for $e< e_E$, it describes non-extremal black hole with two horizons.
  Despite the complicated solution, the thermodynamical quantities, like
temperature ($T$), specific heat($C$) and entropy ($S$) associated with the
black hole are obtained exactly. It turns out that the heat capacity diverges
at critical horizon radius $r_+ = r_C$, where the temperature attains maximum
value and the Hawking-Page transition is achievable. Thus, we have an exact
$D$-dimensional regular black holes, when evaporates lead to a thermodynamical
stable remnant.
