To develop a free-running 3D radial whole-heart multiecho gradient echo (ME-GRE) framework for cardiac- and respiratory-motion-resolved fat fraction (FF) quantification. (NTE = 8) readouts optimized for water-fat separation and quantification were integrated within a continuous non-electrocardiogram-triggered free-breathing 3D radial GRE acquisition. Motion resolution was achieved with pilot tone (PT) navigation, and the extracted cardiac and respiratory signals were compared to those obtained with self-gating (SG). After extra-dimensional golden-angle radial sparse parallel-based image reconstruction, FF, R2 *, and B0 maps, as well as fat and water images were generated with a maximum-likelihood fitting algorithm. The framework was tested in a fat-water phantom and in 10 healthy volunteers at 1.5 T using NTE = 4 and NTE = 8 echoes. The separated images and maps were compared with a standard free-breathing electrocardiogram (ECG)-triggered acquisition. The method was validated in vivo, and physiological motion was resolved over all collected echoes. Across volunteers, PT provided respiratory and cardiac signals in agreement (r = 0.91 and r = 0.72) with SG of the first echo, and a higher correlation to the ECG (0.1% of missed triggers for PT vs. 5.9% for SG). The framework enabled pericardial fat imaging and quantification throughout the cardiac cycle, revealing a decrease in FF at end-systole by 11.4% ± 3.1% across volunteers (p < 0.0001). Motion-resolved end-diastolic 3D FF maps showed good correlation with ECG-triggered measurements (FF bias of -1.06%). A significant difference in free-running FF measured with NTE = 4 and NTE = 8 was found (p < 0.0001 in sub-cutaneous fat and p < 0.01 in pericardial fat). Free-running fat fraction mapping was validated at 1.5 T, enabling ME-GRE-based fat quantification with NTE = 8 echoes in 6:15 min.