Magnetic resonance fingerprinting (MRF) is highly promising as a quantitative MRI technique due to its accuracy, robustness, and efficiency. Previous studies have found high repeatability and reproducibility of 2D MRF acquisitions in the brain. Here, we have extended our investigations to 3D MRF acquisitions covering the whole brain using spiral projection k-space trajectories. Our travelling head study acquired test/retest data from the brains of 12 healthy volunteers and 8 MRI systems (3 systems at 3 T and 5 at 1.5 T, all from a single vendor), using a study design not requiring all subjects to be scanned at all sites. The pulse sequence and reconstruction algorithm were the same for all acquisitions. After registration of the MRF-derived PD T1 and T2 maps to an anatomical atlas, coefficients of variation (CVs) were computed to assess test/retest repeatability and inter-site reproducibility in each voxel, while a General Linear Model (GLM) was used to determine the voxel-wise variability between all confounders, which included test/retest, subject, field strength and site. Our analysis demonstrated a high repeatability (CVs 0.7-1.3% for T1, 2.0-7.8% for T2, 1.4-2.5% for normalized PD) and reproducibility (CVs of 2.0-5.8% for T1, 7.4-10.2% for T2, 5.2-9.2% for normalized PD) in gray and white matter. Both repeatability and reproducibility improved when compared to similar experiments using 2D acquisitions. Three-dimensional MRF obtains highly repeatable and reproducible estimations of T1 and T2, supporting the translation of MRF-based fast quantitative imaging into clinical applications.