How to move a Subversion repository
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First, back up the repository with svn dump:
svnadmin dump /path/to/repos > repos.dump
Copy the repos.dump file to the new machine.
Log into the new machine and create the repository as your svn user.
svnadmin create /path/to/new/repos
Restore the data with svnadmin load:
svnadmin load /path/to/new/repos < repos.dump
IMPORTANT: Set the permissions. If you don't do this, it's unlikely you will be able to use the repository as you would like.
chown -R svn:svnusers /path/to/new/repos ; chmod -R g+w /path/to/new/repos/db/
Test the new repository by commiting a change. You should not get any permission errors.
Resources:
Tecnical Bits: A Simple Way to Backup and Restore a Subversion Repository (but note the missing permission step)
ArchWiki: Subversion backup and restore (includes stuff you don't need if Subversion is already installed)