The full version is "Bob's your uncle, Fanny's your aunt."
No, it's not. Or at least it wasn't. The Aunt Fanny part is an add on to a phrase that had been around since 1887 to mean "your all set". It dates from when Prime Minister Robert Cecil (a.k.a. Lord Salisbury) decided to appoint Arthur Balfour to the post of Chief Secretary for Ireland, a rather prestigious and sensitive post. Not lost on the British public was the fact that Lord Salisbury was better known to Arthur Balfour as "Uncle Bob." In the resulting furore over what was seen as an act of blatant nepotism, "Bob's your uncle" became a popular sarcastic comment applied to any situation where the outcome was preordained by favouritism. Of course, over time the scandal faded, but the phrase was around to stay - slowly becoming a "no worries" or "you've got it made"
(info from Eric Partridge's Dictionary of Catch Phrases)
Johnny Depp brought the Fanny's your aunt part into greater usage just a few years ago when he used the phrase "Roberts your Uncle, Fanny's your aunt" in Pirates of the Caribbean. Before that it had been suggested it was tacked on from the phrase "My Aunt Fanny" used for something unbelievable. Personally I think "Bobs your uncle, Fanny's your aunt" has a nice little rhythm and I love to use it!
Rosie