  Let $k$ be a field of characteristic $p>0$, and let $W$ be a complete
discrete valuation ring of characteristic $0$ that has $k$ as its residue
field. Suppose $G$ is a finite group and $G^{\mathrm{ab},p}$ is its maximal
abelian $p$-quotient group. We prove that every endo-trivial $kG$-module $V$
has a universal deformation ring that is isomorphic to the group ring
$WG^{\mathrm{ab},p}$. In particular, this gives a positive answer to a question
raised by Bleher and Chinburg for all endo-trivial modules. Moreover, we show
that the universal deformation of $V$ over $WG^{\mathrm{ab},p}$ is uniquely
determined by any lift of $V$ over $W$. In the case when $p=2$ and
$G=\mathrm{D}$ is a $2$-group that is either semidihedral or generalized
quaternion, we give an explicit description of the universal deformation of
every indecomposable endo-trivial $k\mathrm{D}$-module $V$.
