PostgreSQL 11 support is now available in Jira 8.7 along with user anonymization for GDPR compliance and OpenID Connect integration (Data Center). You can read the release notes and download the latest version here.
Support for PostgreSQL 10 for Jira Software, Jira Service Desk and Portfolio for Jira has been available since version 8.6 / 4.6. We're also working on backporting PostgreSQL 10 to the Enterprise Release stream. I will be posting updates about the backport on JRASERVER-65910.
Product Manager, Jira Server and Data Center