  We construct the analogue of the Dirac-Born-Infeld (DBI) action in Weyl
conformal geometry in $d$ dimensions to obtain a Weyl gauge invariant theory.
For $d=4$, in a leading order expansion the DBI action becomes the general Weyl
quadratic gravity action associated to this geometry, that has the same gauge
symmetry; this is broken spontaneously and Einstein-Hilbert gravity is
recovered in the broken phase, with $\Lambda>0$. The series expansion of the
DBI action also contains additional non-polynomial terms that can be generated
at quantum level in Weyl quadratic gravity in $d=4$, by a regularisation that
respects this gauge symmetry. Such a regularisation is automatically provided
by the DBI action in $d$ dimensions. If the Weyl gauge boson of dilatations is
`pure gauge', the DBI action recovers in the leading order the conformal
gravity action plus a locally Weyl invariant dilaton action. All fields are of
geometric origin, with no added matter or compensating Weyl scalars, etc. The
calculation is done in a Weyl {\it gauge covariant} and {\it metric}
formulation of Weyl conformal geometry in $d$ dimensions.
