You can follow the following steps and use mysql driver configuration instead of H2.
http://community.jboss.org/people/bpmn2user/blog/2011/01/21/test
Also here is an example using Tomcat and Oracle
http://community.jboss.org/people/bpmn2user/blog/2011/02/26/orcale-integration-with-jbpm5
Modify TOMCAT_HOME/conf/context.xml, TOMCAT_HOME/conf/resource.properties etc to have your MySQL details.