Global warming-induced extreme tropical storms disrupt the operation of offshore wind farms, causing wind power ramp events and threatening the safety of the interconnected onshore grid. In order to attenuate the impact of these ramps, this paper proposes an integrated strategy for forecasting and controlling ramps in offshore wind farms. First, the characteristics of wind power ramps during tropical storms are studied, and a general ramp control framework is established. Second, a wind power ramp prediction scheme is designed based on a minimal gated memory network (MGMN). Third, by taking into account the wind power ramp prediction results and wind power uncertainties, a chance-constraint programming-based optimal ramp control scheme is developed to simultaneously maximize wind power absorption and minimize ramp control costs. Finally, we use real-world offshore wind farm data to validate the effectiveness of the proposed strategy.