We here report on the direct observation of ferroelectric properties of water ice in its 2D phase. Upon nanoelectromechanical confinement between two graphene layers, water forms a 2D ice phase at room temperature that exhibits a strong and permanent dipole which depends on the previously applied field, representing clear evidence for ferroelectric ordering. Characterization of this permanent polarization with respect to varying water partial pressure and temperature reveals the importance of forming a monolayer of 2D ice for ferroelectric ordering which agrees with ab-initio and molecular dynamics simulations conducted. The observed robust ferroelectric properties of 2D ice enable novel nanoelectromechanical devices that exhibit memristive properties. A unique bipolar mechanical switching behavior is observed where previous charging history controls the transition voltage between low-resistance and high-resistance state. This advance enables the realization of rugged, non-volatile, mechanical memory exhibiting switching ratios of 106, 4 bit storage capabilities and no degradation after 10,000 switching cycles., Ferroelectric ordering of water has been at the heart of intense debates due to its importance in enhancing our understanding of the condensed matter. Here, the authors observe ferroelectric properties of water ice in a two dimensional phase under confinement between two graphene layers.