Created branch in wrong place... how to fix?

Hi, I created a branch in a project and did a series of commits. I now discover that I really wanted to make all those changes against a completely different branch of the same project. There shouldn't be any issues as the branch introduces entirely new files (no changes to existing code). I'm struggling to see a way to do this without loosing the history. Some Google'ing suggests 'rebase --onto' but I'm struggling to see how this works or if it is appropriate. Any pointers much appreciated :) Thanks.