In addition to @Jason's answer I had to do a bit more to get my app to run.
Download & unzip Eclipse IDE for Java EE Developers (Note the EE edition)
Download & unzip Eclipse's Web Tools Platform Stable (Milestone) 3.6+
Overwrite the two folders in the Eclipse IDE, with the WTP folder(s) (features & plugins folders)
Download and unzip Tomcat 8
In eclipse new -> other -> server -> Tomcat 8 (choose the unzipped location)
If you get a 404, click the Tomcat 8 in the Servers view -> Server Locations -> Change to Use Tomcat installation, and change the Deploy path: to webapps *
(If you can't edit this, delete any published webapps)