Bangladesh has been ranked as one of the world’s top countries affected by climate change, particularly in terms of agricultural crop sector. The purpose of this study is to identify spatial and temporal changes and trends in long-term climate at local and national scales, as well as their implications for rice yield. In this study, Modified Mann-Kendall and Sen’s slope tests were used to detect significant trends and the magnitude of changes in temperature and rainfall. The temperature and rainfall data observed and recorded at 35 meteorological stations in Bangladesh over 65-years in the time span between the years 1949 and 2013 have been used to detect these changes and trends of variation. The results show that mean annual Tmean, Tmin, and Tmax have increased significantly by 0.13°C, 0.13°C, and 0.13°C/decade, respectively. The most significant increasing trend in seasonal temperatures for the respective Tmean, Tmin, and Tmax was 0.18°C per decade (post-monsoon), 0.18°C/decade (winter), and 0.23°C/decade (post-monsoon), respectively. Furthermore, the mean annual and pre-monsoon rainfall showed a significant increasing trend at a rate of 4.20 mm and 1.35 mm/year, respectively. This paper also evaluates climate variability impacts on three major rice crops, Aus, Aman, and Boro during 1970–2013. The results suggest that crop yield variability can be explained by climate variability during Aus, Aman, and Boro seasons by 33, 25, and 16%, respectively. Maximum temperature significantly affected the Aus and Aman crop yield, whereas rainfall significantly affected all rice crops’ yield. This study sheds light on sustainable agriculture in the context of climate change, which all relevant authorities should investigate in order to examine climate-resilient, high-yield crop cultivation.