This paper proposes a rate adaptation design for high altitude platform (HAP)-aided relaying satellite hybrid free-space optical/radio-frequency (FSO/RF) systems. The design allows switching between two links gradually to reduce the fre- quent link switching in error-prone environments of conventional fixed-rate hybrid FSO/RF systems. System performance metrics, including average transmission rate and outage probability, are analytically studied under the presence of clouds and fading of FSO and RF channels modeled respectively by Gamma-Gamma and Rician distributions. The numerical results quantitatively highlight the effectiveness of our proposed systems over the conventional ones. Moreover, Monte-Carlo simulations are also performed to validate the accuracy of the analytical model.