Unusual secondary relaxations were revealed in metallic glasses (MGs) recently. In this paper, we explore the structural origins of secondary relaxations in La-based MGs alloyed with different species of elements. With the combination of synchrotron X-ray diffraction and ab initio molecular dynamics simulations, solute-atom-centered clusters with a string-like type of medium-range order are found in the MGs, the formation of which leaves dispersed low-electron-density regions. It is found the activation energy of fast secondary relaxation increases with the reduction of low-electron-density regions, while slow secondary relaxation relates to the distance of La in next nearest La-La atomic pairs and the size of the string-like solute-atom-centered clusters. The phenomena are interpreted within the framework of the generalized Maxell model and free volume model. Our results demonstrate fast secondary relaxation as the activation of a small concentration of liquid-like regions with extremely low viscosities preceding slow secondary relaxation, and provide evidence for the correlation of secondary relaxations with short- to medium-range electronic and atomic structure in MGs.