Supernova remnants (SNRs) are believed to be the main sources of Galactic cosmic rays. Molecular clouds associated with SNRs can produce gamma-ray emission through the interaction of accelerated particles with the concentrated gas. The middle aged SNR W28, for its associated system of dense molecular clouds, provides an excellent opportunity to test this hypothesis. We present the AGILE/GRID observations of SNR W28, and compare them with observations at other wavelengths (TeV and 12CO J=1-->0 molecular line emission). The gamma-ray flux detected by AGILE from the dominant source associated with W28 is (14 +- 5) 10^-8 ph cm^-2 s^-1 for E > 400 MeV. This source is positionally well correlated with the TeV emission observed by the HESS telescope. The local variations of the GeV to TeV flux ratio suggest a difference between the CR spectra of the north-west and south molecular cloud complexes. A model based on a hadronic-induced interaction and diffusion with two molecular clouds at different distances from the W28 shell can explain both the morphological and spectral features observed by AGILE in the MeV-GeV energy range and by the HESS telescope in the TeV energy range. The combined set of AGILE and H.E.S.S. data strongly support a hadronic model for the gamma-ray production in W28.