The licence that covers rsync itself

rsync is free software under the GNU General Public License, version 3. The project's own README states it plainly:

“Rsync may be used, modified and redistributed only under the terms of the GNU General Public License, found in the file COPYING in this distribution, or at the Free Software Foundation.”

The full text is in COPYING, and the same licence is on the project's own site as GPL.html. Distributing rsync as part of something else generally carries the GPL's obligations — most importantly, making the corresponding source available to whoever you give the binary to.

The one exception: OpenSSL and xxhash

GPLv3 and the OpenSSL licence aren't compatible in the usual way, so COPYING carves out a specific exception for those two libraries:

“As a special exception, the copyright holders give permission to dynamically link rsync with the OpenSSL and xxhash libraries when those libraries are being distributed in compliance with their license terms, and to distribute a dynamically linked combination of rsync and these libraries. This is also considered to be covered under the GPL's System Libraries exception.”

It covers dynamic linking specifically — the exception doesn't say anything about linking the two statically.

Code bundled inside rsync has its own licence

rsync's source tree carries two third-party libraries, and each keeps the licence its own project ships it under rather than being folded into rsync's GPL:

zlib

The zlib licence: permissive, no attribution required in a product that uses it (though appreciated), altered source must be marked as such, and the licence notice can't be removed from the source.

popt

An MIT/X11-style licence from Red Hat Software, 1998: explicitly permits commercial use, sublicensing and selling, and asks only that the copyright notice be kept.

What this means in practice

Putting the three together, for someone building a new product around rsync or distributing one that bundles it: rsync's own code is under GPLv3, so redistributing it generally means honouring the GPL's source-availability terms; the bundled zlib and popt code carries its own, separately more permissive terms that also need to be honoured; and OpenSSL and xxhash specifically may be dynamically linked and distributed under the exception above, without that link being treated as GPL-incompatible.

None of this is legal advice — it's a reading of what the project's own files say, checked against the files themselves rather than assumed. If it matters for something you're shipping, read COPYING yourself rather than relying on a summary, this one included.