With the recently released Ubuntu 19.10 there is initial support for the Raspberry Pi 4 single-board computers sans the highest-tier 4GB version that embarrassingly suffers from USB ports not working with the current Ubuntu 19.10 build. Fortunately, Canonical is working to address that issue with the RPi4 4GB version as well as making other Raspberry Pi support improvements.
Ubuntu 19.10 should work well on the Raspberry Pi 1GB and 2GB models while the 4GB version doesn't have USB ports working with the current Ubuntu Eoan packages. They have discovered a workaround of using total_mem=3072 for limiting the kernel to just 3GB of RAM in order to get USB functionality. But Canonical is working on proper updates to push out for enabling full USB support on the 4GB Raspberry Pi 4.
Additionally, Canonical is working to support the Raspberry Pi 4 with Ubuntu Server 18.04 LTS in its next HWE update. Further out in the future will also be Ubuntu Core support for the Raspberry Pi 4.