expression — slang, informal
denoting completion of a task, ease of completion, or satisfaction.
The phrase Bob's your uncle is likely a preservation from British English, possibly Cockney English, yet one that is not used in distinct ways in Canada. According to internet searches the expression is used in many former British colonies (see Chart 1). The term is used in ways characteristic of informal speech in Inner Circle varieties more generally (Inner Circle as defined by Kachru (1985), the countries that have predominantly first language speakers of English, usually the UK, Canada, the US, Australia, New Zealand). Many theories exist as to the origin of the phrase, a popular one being that it refers to the appointment of Arthur Balfour to the position of Chief Secretary of Ireland by his uncle Robert Cecil (see, e.g. the 1997 quotation). The origins, however, remain unknown. OED-3 lists the earliest citation for Bob's your uncle from Partridge's 1937 slang dictionary (see OED-3, s.v. "Bob (n7, 3.) - Bob's your uncle").
See also COD-2, s.v. "Bob", which is marked "Cdn & Brit.".
- Used in many Inner Circle varieties of English. Not meeting any of the requirements of Canadianness in DCHP-2 (see Dollinger 2015c).
- 1970  I'm beginning to get the idea, and to start to whistle when the attacking team makes a sloppy kick out of bounds. After all, you've heard of 10-goal polo players? I am now a one-goal spectator. I plan to be insufferable in the Rams' press box all season. "But, really, if you want to see a kicker, I mean, bash on, you should see the goalie England have." A pass pattern may find me stifling a yawn. "Oh, yes, good and all that. But, now, you should see Bobby Charlton, after all." I may even get a Manchester United pocket patch. And Bob's your uncle.
- 1980  Office space being built so fast, it's 'Bob's your uncle.' 
- 1993  Taylor could then hop the Zurich-Toronto
flight, and Bob's your uncle.
- 1997  THIS week, Collected Wisdom dons its deerstalker hat, fills its meerschaum pipe (we never inhale) and follows a line of investigation that leads to the highest echelons of Victorian society.
The question: What is the origin, asked Gordon Young of Kingston, of the phrase "Bob's your uncle."
The answer: This expression, which means "You've got it made," or "You're all set," originated in Britain around 1886 or 1887, reports Jason McKeag of Elmira, Ont.
"At that time, British Prime Minister Robert Cecil (a.k.a. Lord Salisbury) appointed Arthur Balfour as Chief Secretary for Ireland -- which was considered a very high honour. Robert, however, was Arthur's uncle, and the appointment was seen as blatant nepotism. Thus, the phrase 'Bob's your uncle' became a cynical political gibe for any similar act of favouritism. The scandal died down, but the expression didn't, although it has since lost its sarcastic edge." 
- 2000  Every Canadian of British heritage seems to have had an Uncle Bob. No doubt, you've heard the British saying Bob's Your Uncle? Well, the phrase is not mere poppycock. In England, a man named Bob is certain to be somebody's uncle. 
- 2013  Shale gas down there - under Broadway? I mean, I'm no geologist or anything but the stuff is everywhere. Isn't it just a matter of pumping enough water and sand and chemicals deep enough into the ground and boom, Bob's your uncle - the gas comes out? 
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Chart 1: Internet Domain Search, 9 Oct. 2013