PurposeDevelop a novel low‐rank motion‐corrected (LRMC) reconstruction for nonrigid motion‐corrected MR fingerprinting (MRF).MethodsGeneralized motion‐corrected (MC) reconstructions have been developed for steady‐state imaging. Here we extend this framework to enable nonrigid MC for transient imaging applications with varying contrast, such as MRF. This is achieved by integrating low‐rank dictionary‐based compression into the generalized MC model to reconstruct MC singular images, reducing motion artifacts in the resulting parametric maps. The proposed LRMC reconstruction was applied for cardiac motion correction in 2D myocardial MRF (T₁ and T₂) with extended cardiac acquisition window (~450 ms) and for respiratory MC in free‐breathing 3D myocardial and 3D liver MRF. Experiments were performed in phantom and 22 healthy subjects. The proposed approach was compared with reference spin echo (phantom) and with 2D electrocardiogram‐triggered/breath‐hold MOLLI and T₂ gradient‐and–spin echo conventional maps (in vivo 2D and 3D myocardial MRF).ResultsPhantom results were in general agreement with reference spin‐echo measurements, presenting relative errors of approximately 5.4% and 5.5% for T₁ and short T₂ (<100 ms), respectively. The proposed LRMC MRF reduced residual blurring artifacts with respect to no MC for cardiac or respiratory motion in all cases (2D and 3D myocardial, 3D abdominal). In 2D myocardial MRF, left‐ventricle T₁ values were 1150 ± 41 ms for LRMC MRF and 1010 ± 56 ms for MOLLI; T₂ values were 43.8 ± 2.3 ms for LRMC MRF and 49.5 ± 4.5 ms for T₂ gradient and spin echo. Corresponding measurements for 3D myocardial MRF were 1085 ± 30 ms and 1062 ± 29 ms for T₁, and 43.5 ± 1.9 ms and 51.7 ± 1.7 ms for T₂. For 3D liver, LRMC MRF measured liver T₁ at 565 ± 44 ms and liver T₂ at 35.4 ± 2.4 ms.ConclusionThe proposed LRMC reconstruction enabled generalized (nonrigid) MC for 2D and 3D MRF, both for cardiac and respiratory motion. The proposed approach reduced motion artifacts in the MRF maps with respect to no motion compensation and achieved good agreement with reference measurements.