1. In the Artifactory instance via terminal navigate to $ARTIFACTORY_HOME/etc/ and open the artifactory.config.latest.xml file. 
2. Search the line for property urlBase
3. Edit the value for this property to point to the new URL as <urlBase>http://<Artifactory_Server:port>/artifactory</urlBase>
4. Rename the file $ARTIFACTORY_HOME/etc/artifactory.config.latest.xml to  $ARTIFACTORY_HOME/etc/artifactory.config.import.xml
5. Make sure your DNS name is configured to point to the new URL of Artifactory. 
6. Restart Artifactory (for high availability setup a rolling restart is required).