All of our deployments use Chef to manage the Jenkins instance. As a result all plugins get installed using the Jenkins CLI install-plugin command. When installed this way, the groovy plugin always ends up installed but with no hudson.plugins.groovy.GroovyInstaller file under <jenkins-home>/updates. This results in symptoms exactly like those reported in JENKINS-6085, including builds failing with the "Invalid tool ID" error.

I have found that the solution is to go to the plugin-management/advanced tab and click the "Check Now" button to check for updates. This populates the needed file.

I have never used the UI to install the groovy plug-in but I presume that this problem does not present itself in that situation or it would likely have been reported already.