  We find an exact type IIB supergravity solution that represents a
one-parameter deformation of the T-dual of the AdS_5 x S^5 background (with
T-duality applied in all 6 abelian bosonic isometric directions). The
non-trivial fields are the metric, dilaton and RR 5-form only. The latter has
remarkably simple "undeformed" form when written in terms of a
"deformation-rotated" vielbein basis. An unusual feature of this solution is
that the dilaton contains a linear dependence on the isometric coordinates of
the metric precluding a straightforward reversal of T-duality. If we still
formally dualize back, we find exactly the metric, B-field and product of
dilaton with RR field strengths as recently extracted from the eta-deformed
AdS_5 x S^5 superstring action in arXiv:1507.04239. We also discuss similar
solutions for deformed AdS_n x S^n backgrounds with n=2,3. In the eta -> i
limit we demonstrate that all these backgrounds can be interpreted as special
limits of gauged WZW models and are also related to (a limit of) the
Pohlmeyer-reduced models of the AdS_n x S^n superstrings.
