Resilio Sync (formerly Bittorrent Sync) pretty much offers that. They use relays in case both peers cannot pierce NAT, but the relays only see ciphertext. They also have apps for Android and iOS, making transfers to mobile devices also possible. Since it is closed-source software, it's up to you to decide whether you trust the software.
SyncThing is a free software alternative, but I wouldn't say that it is usable (yet) for the average user.