Over the years, several attempts were made to establish the possible link by which solar activity influenced climate change. However, the physical mechanism for these relationships has been the major challenge. In this research, we investigate the relationship between solar/geomagnetic activity and cosmic rays, the connection between cosmic rays and cloud covers and finally, cloud covers and climatic parameters. This is the proposed physical mechanism used in this study to investigate how solar activity influenced climate change in Nigeria. Sunspot number, aa index, galactic cosmic rays (GCRs), rainfall and maximum temperature data were used in this study. The time period under investigation in this study spanned for 63 years (1950-2012). Spearman's rank correlation technique was employed in analyzing the data. Results reveal that sunspot number and aa index varied in the opposite direction with GCRs based on the 11-year solar cycle. This inverse relationship was confirmed from the correlation analysis. This depicts that solar and geomagnetic activities modulate cosmic rays penetrating into the Earth's atmosphere. Furthermore, the relationship between cosmic rays and cloud covers is yet to be fully ascertained in this study. This has limited the proposed physical mechanism that this study hoped to establish. However, the variations of cloud covers with rainfall and temperature show that changes in cloud covers are associated with changes in rainfall and temperature. This study has given useful information on the possible links by which solar activity could influence climate change.