Wetland ecosystems in the Qinghai–Tibet Plateau are pivotal for global ecology and regional sustainability. This study investigates the dynamic changes in wetland ecosystems within the Chaidamu Basin and their response to drought, aiming to foster sustainable wetland utilization in the Qinghai–Tibet Plateau. Using Landsat TM/ETM/OLI data on the Google Earth Engine platform, we employed a random forest (RF) method for annual long-term land cover classification. Standardized precipitation evapotranspiration indices (SPEI3, SPEI6, SPEI9, and SPEI12) on different time scales were used to assess meteorological drought conditions. We employed a Pearson correlation analysis to examine the relationship between wetland changes and various SPEI scales. The BFASAT method was used to evaluate the impact of SPEI12 trends on the wetlands, while a cross-wavelet analysis explored teleconnections between SPEI12 and atmospheric circulation factors. Our conclusion is as follows: The wetlands, including lake, glacier, and marsh wetlands, exhibited a noticeable increasing trend. Wetland expansion occurred during specific periods (1990–1997, 1998–2007, and 2008–2020), featuring extensive conversions between wetlands and other types, notably the conversion from other types to wetlands. Spatially, lake and marsh wetlands predominated in the low-latitude basin, while glacier wetlands were situated at higher altitudes. There were significant negative correlations between the SPEI at various scales and the total wetland area and types. SPEI12 displayed a decreasing trend with non-stationarity and distinct breakpoints in 1996, 2002, and 2011, indicating heightened drought severity. Atmospheric circulation indices (ENSO, NAO, PDO, AO, and WP) exhibited varying degrees of resonance with SPEI12, with NAO, PDO, AO, and WP demonstrating longer resonance times and pronounced responses. These findings underscore the significance of comprehending wetland changes and drought dynamics for effective ecological management in the Chaidamu Basin of the Qinghai–Tibet Plateau.