  Given a collection $\{ G_i\}_{i=1}^d$ of finite groups and a ring $R$, we
define a subring of the ring $M_n(R)$ ($n = \sum_{i=1}^d|G_i|)$ that
encompasses all the individual group rings $R[G_i]$ along the diagonal blocks
as $G_i$-circulant matrices. The precise definition of this ring was inspired
by a construction in graph theory known as the joined union of graphs. We call
this ring the join of group rings and denote it by $\mathcal{J}_{G_1,\dots,
G_d}(R)$. In this paper, we present a systematic study of the algebraic
structure of $\mathcal{J}_{G_1,\dots, G_d}(R)$. We show that it has a ring
structure and characterize its center, group of units, and Jacobson radical.
When $R=k$ is an algebraically closed field, we derive a formula for the number
of irreducible modules over $\mathcal{J}_{G_1,\dots, G_d}(k)$. We also show how
a blockwise extension of the Fourier transform provides both a generalization
of the Circulant Diagonalization Theorem to joins of circulant matrices and an
explicit isomorphism between the join algebra and its Wedderburn components.
