Tested on Ubuntu 16.04 LTS with Unity 7 desktop.
Download official Linux 64-bit binary package from https://desktop.telegram.org/.
Extract to /opt/Telegram (version is latest as of this writing):
sudo tar xJf tsetup.1.2.17.tar.xz -C /opt/
Launch as user from $HOME:
myser:~$ /opt/Telegram/Telegram
Lock to Launcher.
Copy telegramdesktop.desktop from ~/.local/share/applications to ~/.config/autostart:
cp ~/.local/share/applications/telegramdesktop.desktop ~/.config/autostart
Log out and then in again.