Thermosphere densities near 410 km altitude inferred from accelerometer measurements on the Challenging Minisatellite Payload (CHAMP) satellite are analyzed for solar irradiance variability effects during the period 2002–2004. Correlations between the densities and the solar irradiances for different spectral lines and wavelength ranges reveal significantly different characteristics. The density correlates remarkably well with all the selected solar irradiances except the lower chromospheric O I (130.4 nm) emission. Among the chosen solar proxies, the Mg II core‐to‐wing ratio index, EUV (30–120 nm) and F10.7 show the highest correlations with the density for short‐term (<∼27 d) variations. For both long‐term (>∼27 d) and short‐term variations, linear correlation coefficients exhibit a decreasing trend from low latitudes toward high latitudes. The density variability can be effectively modeled (capturing 71% of the variance) using multiple solar irradiance indices, including F10.7, SEUV (the EUV 30–120 nm index), and SFUV (the FUV 120–193 nm index), in which a lag time of 1 d was used for both F10.7 and SEUV, and 5 d for SFUV. In our regression formulation, SEUV has the largest contribution to the density variation (40%), with the F10.7 having the next largest contribution (32%) and SFUV accounting for the rest (28%). Furthermore, a pronounced period of about 27.2 d (mean period of the Sun's rotation) is present in both density and solar irradiance data of 2003 and 2004, and a pronounced period of about 54.4 d (doubled period of the solar rotation) is also revealed in 2004. However, soft X‐ray and FUV irradiances did not present a pronounced 54.4‐d period in 2004, in spite of their high correlation with the densities. The Ap index also shows 54‐d periodicities in 2004, and magnetic activity, together with solar irradiance, affects the 54‐d variation in density significantly. In addition, NRLMSISE00, DTM‐2000, and JB2006 model predictions are compared with density measurements from CHAMP to assess their accuracy, and the results show that these models underestimate the response of the thermosphere to variations induced by solar rotation.