The latest 2.24 release of the Nimbus JOSE + JWT library removes the Apache Commons Codec dependency for base 64 and base 64 URL-safe encoding / decoding, by switching to an internal codec (from the migbase64 project). This should greatly ease use of the library on Android devices.
Thanks to everyone who contributed with patches and suggestions (and endured the long wait J ).
The new release should reach Maven Central by the end of today. Alternatively, you can get a copy of the library JAR from the download section of the git repo.