  We study the weak convergence of $\beta$- and $\beta'$-Delaunay tessellations
in $\mathbb{R}^{d-1}$ that were introduced in part I of this paper, as
$\beta\to\infty$. The limiting stationary simplicial random tessellation, which
is called the Gaussian-Delaunay tessellation, is characterized in terms of a
space-time paraboloid hull process in $\mathbb{R}^{d-1}\times\mathbb{R}$. The
latter object has previously appeared in the analysis of the number of shocks
in the solution of the inviscid Burgers' equation and the description of the
local asymptotic geometry of Gaussian random polytopes. In this paper it is
used to define a new stationary random simplicial tessellation in
$\mathbb{R}^{d-1}$. As for the $\beta$- and $\beta'$-Delaunay tessellation, the
distribution of volume-power weighted typical cells in the Gaussian-Delaunay
tessellation is explicitly identified, establishing thereby a new bridge to
Gaussian random simplices. Also major geometric characteristics of these cells
such as volume moments, expected angle sums and also the cell intensities of
the Gaussian-Delaunay tessellation are investigated.
