Most important things first: if you intend to use rsyslog inside a GPLv3 compatible project, you are free to do so. You don't even need to continue reading. If you intend to use rsyslog inside a non-GPLv3 compatible project, rsyslog offers you some liberties to do that, too. However, you then need to study the licensing details in depth.
The project hopes this is a good compromise, which also gives a boost to fellow free software developers who release under GPLv3.
And now on to the dirty and boring license details, still on a executive summary level. For the real details, check source files and the files COPYING and COPYING.LESSER inside the distribution.
The rsyslog package contains several components:
- the rsyslog core programs (like rsyslogd)
- plugins (like imklog, omrelp, ...)
- the rsyslog runtime library
Each of these components can be thought of as individual projects. In fact, some of the plugins have different main authors than the rest of the rsyslog package. All of these components are currently put together into a single "rsyslog" package (tarball) for convinience: this makes it easier to distribute a consistent version where everything is included (and in the right versions) to build a full system. Platform package maintainers in general take the overall package and split off the individual components, so that users can install only what they need. In source installations, this can be done via the proper ./configure switches.
However, while it is convenient to package all parts in a single tarball, it does not imply all of them are necessarily covered by the same license. Traditionally, GPL licenses are used for rsyslog, because the project would like to provide free software. GPLv3 has been used since around 2008 to help fight for our freedom. All rsyslog core programs are released under GPLv3. But, from the beginning on, plugins were separate projects and we did not impose and license restrictions on them. So even though all plugins that currently ship with the rsyslog package are also placed under GPLv3, this can not taken for granted. You need to check each plugins license terms if in question - this is especially important for plugins that do NOT ship as part of the rsyslog tarball.
In order to make rsyslog technology available to a broader range of applications, the rsyslog runtime is, at least partly, licensed under LGPL. If in doubt, check the source file licensing comments. As of now, the following files are licensed under LGPL: