No mystery here, I think. All that "Bob's your uncle" means is "and there you have it" or perhaps "voila!". It's a British expression, well-documented in British English A to Zed (which is where I learned it).

I've heard Brits construct elaborate references to the basic phrase, e.g. "And Robert's your father's brother"...

No one knows for sure where this expression came from originally, but a popular theory is that it derives from an incident in 1887 when Conservative British Prime Minister Robert "Bob" Cecil, in a brazen act of nepotism, appointed his own nephew Arthur Balfour to a plum posting as Chief Secretary for Ireland. This move was surprising and received widespread condemnation, given that Balfour's only relevant qualification seemed to be that Bob was his uncle.

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