iMovie projects cannot be independently moved. They must reside in an iMovie library. So, you would need to move the library that contains the project or create a new library and copy your projects over to it and then move that library. You need a thumb drive, or other external drive, that is formatted Mac OS Extended (Journaled) to accomplish the transfer. In other words, you move or copy the library that contains the projects to the external drive and then plug the external drive into your new Mac where you can access them. The new Mac must be running the exact same version of iMovie that was used to create the projects, because if you update the projects with a newer version on your new Mac you won't be able to play them in the same library on your old Mac. So keep a back up of your original library if you think you might want to play or edit them on your old Mac.
It is always safer to copy rather than move projects and libraries until you are sure that everything is working. Back up your library first. Also, be aware that reformatting a drive erases all data on it, so first back up any data that you want to keep.
-- Rich