Steps followed -
1. Download REST API war (camunda-engine-rest-7.4.0-tomcat.war) from https://app.camunda.com/nexus/content/groups/public/org/camunda/bpm/camunda-engine-rest/
2. Put it in webapps folder of Tomcat
3. Start Tomcat.
Dec 18, 2015 11:23:19 AM org.apache.catalina.core.StandardContext filterStart
SEVERE: Exception starting filter Resteasy
java.lang.NoClassDefFoundError: org/camunda/bpm/engine/ProcessEngineException
at java.lang.Class.getDeclaredConstructors0(Native Method)
at java.lang.Class.privateGetDeclaredConstructors(Class.java:2671)
at java.lang.Class.getConstructors(Class.java:1651)
at org.jboss.resteasy.util.PickConstructor.pickSingletonConstructor(PickConstructor.java:30)
at org.jboss.resteasy.spi.ResteasyProviderFactory.getProviderInstance(ResteasyProviderFactory.java:1136)
at org.jboss.resteasy.spi.ResteasyProviderFactory.addExceptionMapper(ResteasyProviderFactory.java:598)
at org.jboss.resteasy.spi.ResteasyProviderFactory.registerProvider(ResteasyProviderFactory.java:856)
at org.jboss.resteasy.spi.ResteasyProviderFactory.registerProvider(ResteasyProviderFactory.java:820)
at org.jboss.resteasy.spi.ResteasyDeployment.registration(ResteasyDeployment.java:334)
at org.jboss.resteasy.spi.ResteasyDeployment.start(ResteasyDeployment.java:233)
at org.jboss.resteasy.plugins.server.servlet.ServletContainerDispatcher.init(ServletContainerDispatcher.java:67)
at org.jboss.resteasy.plugins.server.servlet.FilterDispatcher.init(FilterDispatcher.java:39)
at org.apache.catalina.core.ApplicationFilterConfig.initFilter(ApplicationFilterConfig.java:279)
at org.apache.catalina.core.ApplicationFilterConfig.getFilter(ApplicationFilterConfig.java:260)
at org.apache.catalina.core.ApplicationFilterConfig.<init>(ApplicationFilterConfig.java:105)
at org.apache.catalina.core.StandardContext.filterStart(StandardContext.java:4841)
at org.apache.catalina.core.StandardContext.startInternal(StandardContext.java:5535)
at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:150)
at org.apache.catalina.core.ContainerBase.addChildInternal(ContainerBase.java:901)
at org.apache.catalina.core.ContainerBase.addChild(ContainerBase.java:877)
at org.apache.catalina.core.StandardHost.addChild(StandardHost.java:652)
at org.apache.catalina.startup.HostConfig.deployDirectory(HostConfig.java:1263)
at org.apache.catalina.startup.HostConfig$DeployDirectory.run(HostConfig.java:1948)
at java.util.concurrent.Executors$RunnableAdapter.call(Executors.java:511)
at java.util.concurrent.FutureTask.run(FutureTask.java:266)
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1142)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:617)
at java.lang.Thread.run(Thread.java:745)
Caused by: java.lang.ClassNotFoundException: org.camunda.bpm.engine.ProcessEngineException
at org.apache.catalina.loader.WebappClassLoader.loadClass(WebappClassLoader.java:1858)
at org.apache.catalina.loader.WebappClassLoader.loadClass(WebappClassLoader.java:1709)
... 28 more