EteSync is a secure, end-to-end encrypted, and privacy respecting sync for your contacts, calendars and tasks. It's fully open-source (clients and server), with clients available for Android, iOS, the desktop and the web.
The EteSync Android client can populate Tasks with data, or you can enter your credentials into Tasks and synchronize directly with your EteSync host.
Once your account is signed-in, Tasks will create a Category with your username in the sidebar. Your etesync lists will be kept separately from your local lists. In order to upload your existing lists to etesync, you have to use multi-select + select all + move to migrate the data for each list. For more info, see: issue #1597.