You can also try japicmp, it's a neat project I found recently while trying to perform the same task.
Its usage is pretty simple and it comes down to passing it two versions of your library packaged as JARs... for example:
java -jar japicmp-0.0.2.jar -n my-jar-new.jar -o my-jar-old.jar
It also has an API that allows you to use it programmatically.
The project's Github page has a straightforward guide on how to get started.
Also, this SO answer suggests jarc as an alternative