Short version: the "@" symbol has been around for hundreds of years. It has different names in different cultures. It wasn't on early typewriters but by the 1889 it was. In the 1960s it became part of ASCII, and Ray Tomlinson used it as a symbol for routing email to another computer.
BTW, they show the "@" on the 4 key. That's the British typewriter layout. The US keyboard had a "$" on that position, and "@" was on the same key as ¢, to the right of ";". (I believe ¢ disappeared in ASCII because it could be composed as 'c' + '/'.)
ASCII-1963 did not have Backspace and therefore did not have character composition. The concept of composing accents appeared in ASCII-1965, by which time ¢ was already gone.
> The fact that there is no single word in English for the symbol has prompted some writers to use the French arobase[3] or Spanish and Portuguese arroba, or to coin new words such as asperand,[4] ampersat'[5] and strudel,[6] but none of these has achieved wide usage.
That Wikipedia entry start "ampersat", another term I hadn't heard of.
There's a lot of discussion on the talk page about the various names and neologisms.