Jonathan Levin has released LiberTV, a jailbreak for the Apple TV 4 and tvOS based on yalu by Luca Todesco.
The jailbreak works on tvOS 9.1 through 10.1 but does not work on tvOS 10.1.1. It provides a full set of kernel patches which allow running unsigned code and injecting arbitrary libraries into any tvOS process.
There is no Cydia. The 64-bit version of Mobile Substrate should work but was not included. Saurik could release Cydia for tvOS at some point but no word on whether that will happen yet.
Similar to yalu, the jailbreak comes in the form of an IPA that needs to be signed. It is semi-tethered. The IPA includes a modified 64-bit only bootstrap.tar, containing /bin/sh -> /bin/bash, some tools (in /usr/local/bin), dropbear (a free standing ssh daemon, with its keys in /etc/dropbear), and a few select binaries.
Levin repeatedly warns that after jailbreak you should take great care not to overwrite any system binaries as you could brick your device.
Below is link to download the LiberTV jailbreak from Jonathan Levin for the Apple TV 4 running tvOS.
This software currently supports the jailbreak of tvOS 9.1 to 10.1.