There are various cloud service providers to host Java based web applications.
One such provider is Cloud Bees.
First register for an account with Cloudbees.
It provides an easy way to deploy your (.war) file in Apache Tomcat. You can also deploy it by configuring Jenkins to download and build source from repositories such as github, svn etc.,
It also provides Amazon EC2 server to manage your Mysql DB (minimal version is free).
There are lot of other features provided by this vendor.
Only minimal version is free, you need to pay if you want your application to be scalable.