I was unaware until recently that this word is largely a term used in British English. In fact, until an American friend asked about it, I would have been under the impression that it was used across the English-speaking world, if I had thought about it at all!
I think it will come as no surprise that the word consists of two parts: gob and smack, with the second part in the past participle form smacked.
The first element, gob, is a northern English and also Scottish word meaning “mouth”. It is thought to derive from the Scottish Gaelic word “gob” that means “beak”.
The second part, smack, comes from the Low German smacken “to strike” or “to throw”, and somewhat surprisingly, it is a cognate of the Lithuanian term smogti – “to strike, to hit, deliver a blow”.
Although the earliest written example we have of gobsmacked as a term is only from 1959, it is likely that the word has been used in speech for much longer than that.
Glossologics 
I am from Birmingham. I never heard this word until about 20 years ago when I first met someone from Newcastle. It was one of several words that caused us problems.