Yes, it is possible to use @Transactional on private methods, but as others have mentioned this won't work out of the box. You need to use AspectJ. It took me some time to figure out how to get it working. I will share my results.
I chose to use compile-time weaving instead of load-time weaving because I think it's an overall better option. Also, I'm using Java 8 so you may need to adjust some parameters.
First, add the dependency for aspectjrt.
<dependency>
<groupId>org.aspectj</groupId>
<artifactId>aspectjrt</artifactId>
<version>1.8.8</version>
</dependency>
Then add the AspectJ plugin to do the actual bytecode weaving in Maven (this may not be a minimal example).
<plugin>
<groupId>org.codehaus.mojo</groupId>
<artifactId>aspectj-maven-plugin</artifactId>
<version>1.8</version>
<configuration>
<complianceLevel>1.8</complianceLevel>
<source>1.8</source>
<target>1.8</target>
<aspectLibraries>
<aspectLibrary>
<groupId>org.springframework</groupId>
<artifactId>spring-aspects</artifactId>
</aspectLibrary>
</aspectLibraries>
</configuration>
<executions>
<execution>
<goals>
<goal>compile</goal>
</goals>
</execution>
</executions>
</plugin>
Finally add this to your config class
@EnableTransactionManagement(mode = AdviceMode.ASPECTJ)
Now you should be able to use @Transactional on private methods.
One caveat to this approach: You will need to configure your IDE to be aware of AspectJ otherwise if you run the app via Eclipse for example it may not work. Make sure you test against a direct Maven build as a sanity check.