Purpose: To develop an efficient navigator-based motion and temporal B0 shift correction technique for 3D multi-echo gradient-echo (ME-GRE) MRI for quantitative susceptibility mapping (QSM) and R2* mapping. Theory and Methods: A dual-echo 3D spiral navigator was designed to interleave with the Cartesian ME-GRE acquisitions, allowing the acquisition of both low- and high-echo time signals. We additionally designed a novel conjugate-phase based reconstruction method for the joint correction of motion and temporal B0 shifts. We performed both numerical simulation and in vivo human scans to assess the performance of the methods. Results: Numerical simulation and human brain scans demonstrated that the proposed technique successfully corrected artifacts induced by both head motions and temporal B0 changes. Efficient B0-change correction with conjugate-phase reconstruction can be performed on less than 10 clustered k-space segments. In vivo scans showed that combining temporal B0 correction with motion correction further reduced artifacts and improved image quality in both R2* and QSM images. Conclusion: Our proposed approach of using 3D spiral navigators and a novel conjugate-phase reconstruction method can improve susceptibility-related measurements using MR.