Background: EQ-5D health state utilities (HSU) are commonly used in health economics to compute quality-adjusted life years (QALYs). The EQ-5D, which is country-specific, can be derived directly or by mapping from self-reported health-related quality of life (HRQoL) scales such as the PROMIS-29 profile. The PROMIS-29 from the Patient Reported Outcome Measures Information System is a comprehensive assessment of self-reported health with excellent psychometric properties. We sought to find optimal models predicting the EQ-5D-5L crosswalk from the PROMIS-29 in the United Kingdom, France, and Germany and compared the prediction performances with that of a US model. Methods: We collected EQ-5D-5L and PROMIS-29 profiles and three samples representative of the general populations in the UK (n = 1509), France (n = 1501), and Germany (n = 1502). We used stepwise regression with backward selection to find the best models to predict the EQ-5D-5L crosswalk from all seven PROMIS-29 domains. We investigated the agreement between the observed and predicted EQ-5D-5L crosswalk in all three countries using various indices for the prediction performance, including Bland–Altman plots to examine the performance along the HSU continuum. Results: The EQ-5D-5L crosswalk was best predicted in France (nRMSEFRA = 0.075, nMAEFRA = 0.052), followed by the UK (nRMSEUK = 0.076, nMAEUK = 0.053) and Germany (nRMSEGER = 0.079, nMAEGER = 0.051). The Bland–Altman plots show that the inclusion of higher-order effects reduced the overprediction of low HSU scores. Conclusions: Our models provide a valid method to predict the EQ-5D-5L crosswalk from the PROMIS-29 for the UK, France, and Germany.