The present paper has investigated the associations of solar activity (SA), represented by total solar irradiance (TSI), galactic cosmic rays (GCR) and terrestrial climate parameters in particular the global cloudiness and global surface temperature. To that end, we have analysed thirty five years (1983–2018) data of these parameters and have applied the Granger-causality test in order to assess whether there is any potential predictability power of one indicator to the other. The correlations among the involved parameters are tested using Vector Auto Regression (VAR) model and variance decomposition method. As a result of the above analysis, we have found that the TSI is an important factor and has contributed about 8.77 ± 0.42% in the cosmic ray intensity variations. In case of cloud cover variations, the other three parameters (TSI, cosmic ray and global surface temperature) have played a significant role. Further, the TSI changes have contributed 1.68 ± 0.03% fluctuations in the variance of the cloud cover while the cosmic ray intensity and global surface temperature have contributed about 4.89 ± 0.08% and 10.87 ± 1.41% respectively. In case of the global surface temperature anomaly both TSI and cloud covers have contributed about 5.07 ± 0.47% and 14.42 ± 2.13% fluctuations respectively. Additionally, we have also assessed the impact of internal climate oscillations like multivariate ENSO index (MEI), north Atlantic oscillations (NAO) and quasi biennial oscillations (QBO) on cloud cover variations. The contribution of these internal oscillations e.g. ENSO, NAO and QBO in cloud cover variation were reported as 7.48 ± 1.02%, 5.51 ± 0.16% and 1.36 ± 0.43% respectively.