  We obtain a large class of Lorentzian wormhole spacetimes in scalar-tensor
gravity, for which the matter stress energy does satisfy the weak energy
condition. Our constructions have zero Ricci scalar and an everywhere finite,
non-zero scalar field profile. Interpreting the scalar-tensor gravity as an
effective on-brane theory resulting from a two-brane Randall--Sundrum model of
warped extra dimensions, it is possible to link wormhole existence with that of
extra dimensions. We study the geometry, matter content, gravitational
red-shift and circular orbits in such wormholes and argue that our examples are
perhaps among those which may have some observational relevance in astrophysics
in future. We also study traversability and find that our wormholes are indeed
traversable for values of the metric parameters satisfying the weak energy
condition.
