I checked out some SVN repositories and created a project out of them. After some changes and configuration I found out that I can use git for my SVN repositories. But the only way I found was to clone the repositories with git-svn. Since I already checked out the repositories and worked on them, I'd like to convert the existing repositories. Is it possible? What is the best way?
No, it's not possible. Local checkouts don't contain enough information (branches, tags, history). To convert SVN repo to git one needs access to SVN server or at least a dump from svnadmin dump.
There are many tools and ways to convert SVN to git. See How to migrate SVN repository with history to a new Git repository?
You create authors files that maps SVN login names to git format name <email> and run git svn clone.
There are also other tools similar to git svn. There are svn2git (and fast-export), reposurgeon and other.