Recent climate change has worsened the risk of extreme weather events, among which extreme offshore wind storms threaten secure operation by inducing offshore wind power ramps. Offshore wind power ramps cause the instantaneous power fluctuation of interconnected onshore grids and may lead to unexpected load shedding or generator tripping. In this paper, considering offshore wind power uncertainties, we propose a novel robust coordinated offshore wind power ramp control strategy by dispatching thermal units, energy storage systems, and hydrogen storage systems cooperatively. First, the impact of extreme wind storms on an offshore wind farm output power ramp is analyzed, and the general framework of offshore wind power ramp control is presented based on the two-stage robust optimization considering the dual uncertainties of load demand and wind power. Second, a coordinated wind power ramp control model is established considering the operational characteristics of different ramp control sources such as thermal units, energy storage systems, and offshore wind farms. Third, a robust ramp control strategy is developed using the column-and-constraint generation (CC&G) algorithm. Simulation results show the effectiveness of the proposed ramp control strategy.