From one server to another, no need for file transfers or anything like that. Do this on the new server.
mkdir /foo/bar/new svnadmin create /foo/bar/new ssh firstname.lastname@example.org "svnadmin dump /foo/bar/old" | svnadmin load /foo/bar/new
On your working copies you’ll need to say where the new repository location is:
svn switch --relocate https://old.host/svn https://new.host/svn /path/to/working/copy