BOUT++ is open source under the Lesser General Public License (LGPL), and is available on github. Several versions are available, and can be downloaded as a zip/tar file or using Git.
Most users are advised to use the latest stable version. If you need some recently added feature then you may need to use the development version, though you will run the risk of occasionally getting broken code.
The latest release is always available from here.
Previous releases are available: