With the advancement of measurement technology, the long-term memory (LTM) effect within the degradation data of many assets has recently been detected, which implies that the future degradation process highly correlates with both the current degradation status and historical degradation trajectory across a long time period. To capture the LTM effect, several LTM-integrated degradation models have been developed in the literature. In practice, degradation data are often contaminated with measurement errors, which are ignored in most existing LTM-integrated degradation studies. Without considering measurement errors, the asset degradation modeling and reliability analysis may be biased. In this article, we propose a novel LTM-integrated degradation model that quantitatively incorporates measurement errors. Both fixed-effect and random-effect scenarios of degradation growth are considered. A maximum-likelihood estimation approach is developed to estimate the parameters of the proposed model. Based on this model, asset reliability analysis and lifetime prediction are developed. Simulation studies are implemented to evaluate the performance of the proposed model. A real case study using the capacity degradation data of lithium-ion pouch cells is conducted to illustrate the superiority of the proposed model. Results demonstrate that conventional LTM-integrated degradation models, which ignore the measurement errors, significantly misestimate the uncertainty of asset lifetime.