Third-party apps are great and all, but if you're using GNOME, add a Todoist account in Settings -> Online Accounts and use gnome-todo for a truly native experience.
There is no official client, but their API is public and documented. I use Todoist https://github.com/sachaos/todoist as my daily driver. It has offline support and the integration with peco is sublime.
- http://todoistlinux.hakimouake.com/
- https://github.com/KryDos/todoist-linux
There are also various command line clients, e.g.: https://github.com/sachaos/todoist