Christine Ammer, The American Heritage Dictionary of Idioms (1997) has an entry for out front that contains a mention of out back as well:
out front In front of a building or house, as in We really need to put another light out front, or I'll meet you at the museum, out front. The antonym, referring to the back of building is out back, as in John's out back fixing his bike. The noun front has been used for the side of a building where the main entrance is located since the mid-1300s; back for the rear of a building dates from the late 1300s.
Unfortunately, this isn't much to go on. It seems clear that the idiomatic use of out back and out front is much more common in North American English than in UK English. But I did find a couple of early instances that suggest that the form may have been used in England before it became very common in North America.
From a 1700 translation of Christoph Schewitzer, A Relation of a Voyage To and Thorough the East-Indies, From the Year 1675 to 1683 (1700):
Thus they [the inhabitants of Columbo] go holloing and shooting along the whole day, thro' Woods and over Mountains : At Night they rest, and for fear the Elephants should get out back again, they light Fires all along about a Stone's throw from each other, which the Elephants are very much afraid of.
And from "Minutes of Evidence Taken Before Select Committee on the Carlow Borough Elections Petitions" (July 1839), in British House of Commons, Parliamentary Papers, 1780–1849, volume 7:
[Question:] Was there any appearance in the back yard of any wall running out back from the house having previously existed, and having been pulled down?
[Answer:] No, I did not observe it; I never visited the place but once, and I saw the house just exactly as I describe it to you.
From this meager evidence, it appears that out back is more than 300 years old in English and has been used in England from a fairly early date. Whether settlers from England to North America brought the phrase with them and it then died out in the mother country, or whether it was reinvented in North America independently of earlier usage in Great Britain, I can't tell. Out front flows naturally as an antonym from out back, so once one of them is established, little is needed to obtain the other.