Broadband rotational spectroscopy of water clusters produced in a pulsed molecular jet expansion has been used to determine the oxygen atom geometry in three isomers of the nonamer and two isomers of the decamer. The isomers for each cluster size have the same nominal geometry but differ in the arrangement of their hydrogen bond networks. The nearest neighbor O[BOND]O distances show a characteristic pattern for each hydrogen bond network isomer that is caused by three-body effects that produce cooperative hydrogen bonding. The observed structures are the lowest energy cluster geometries identified by quantum chemistry and the experimental and theoretical O[BOND]O distances are in good agreement. The cooperativity effects revealed by the hydrogen bond O[BOND]O distance variations are shown to be consistent with a simple model for hydrogen bonding in water that takes into account the cooperative and anticooperative bonding effects of nearby water molecules.