A technique provides virtual storage processor (VSP) mobility with induced file system format migration. The technique involves receiving a command specifying (i) a source VSP which includes source file systems which store data in a source file system format, (ii) a destination, and (iii) a destination file system format. The technique further involves forming, in response to the command, a destination VSP which includes destination file systems. The technique further involves copying, while the source VSP is accessed by a set of host computers, data from the source file systems of the source VSP to the destination file systems of the destination VSP. The destination file systems store the copied data in the destination file system format. The technique further involves synchronizing, after the data is copied from the source file systems to the destination file systems, state changes between the source VSP and the destination VSP.