We show that dissociative oxygen adsorption on Ag(001) induces below room temperature a missing row 2 root 2x root 2 reconstruction of the substrate. As demonstrated by the analysis of the photoelectron diffraction patterns, the oxygen atoms sit thereby in a c(2x2) arrangement in the previous fourfold hollow sites nearly coplanar with the Ag atoms, while rows of substrate atoms are removed along the [100] directions. Annealing the crystal above 350 K restores the p(1X1) symmetry and the oxygen moves to 0.6 Angstrom above the fourfold hollow site. It becomes then more oxidic in nature, as demonstrated by the shift of the O1s level from 530.3 eV to 528.3 eV. The phase transition affects also the O2s and O2p levels as well as the surface component of Ag 3d(5/2). The vibrational frequency of the oxygen adatoms against the surface decreases at the phase transition, in accord with the larger adsorption distance. The highs temperature phase is active towards CO and C(2)H(4) oxidation, while the low-temperature phase is nor. When cooling the sample below room temperature the reconstructed phase is restored. The time constant of this process as well as the chemical reactivity of the high-temperature phase are weakly reproducible since they depend on the previous history, i.e., presumably on the subsurface oxygen content of the sample.