My compact version of The Oxford English Dictionary lists it as "An infantile word expressing thanks," and dates its first reference from 1772, unless my eyes deceive me (I am momentarily unable to locate the magnifying glass that came with the tome).
Edit:
Thank god for Eric Partridge.
He quotes the same OED reference, only in larger type.
Here is the entry: Ta! ; rarely taa!
Thanks!
:
coll., orig.
and mainly nursery: 1772, Mrs Delany, 'You would not say "ta" to me for my congratulation,' O.E.D. Ex a young child's difficulty with th and nks .
english.stackexchange.com/users/2303/Robusto
Online Etymology Dictionary says: ta : 1772, "natural infantile sound of gratitude" [Weekley].
Although possibly originating from the imitative of baby talk, this is in widespread use in the North of England and Wales as an informal "thanks" amongst adults.
American Heritage Dictionary of the English Language says: ta :
Chiefly British Used to express thanks.
ETYMOLOGY:
Baby-talk alteration of "thank you".
english.stackexchange.com/users/127/Mehper C. Palavuzlar
When a term originates in northern English dialects as "ta" appears to, I often begin by looking at nordic languages as much of northern England was conquered by the Vikings and the parts of the language endure both in words and in the overall sound - if you listen the geordie accent has a definite scandinavian cadence to it.
Looking at modern Danish and Norwegian
we see that "Thanks" translates as "Tak" or "Takk" respectively, so it seems to me quite plausible that this provides an origin for "Ta".
english.stackexchange.com/users/1725/glenatron
I would have said it was just a shortening of "thanks".
It was in common use in the days of my youth in Northern England.
It's also used as an abbreviation for "thanks" in internet chat rooms.
english.stackexchange.com/users/2254/Tom Bell
As an Australian I can say 'ta' is used extensively in Australia.
I can't comment on other explanatios as I am not a language expert.
However I would like to suggest, as that many caucasian Australians are of Celtic ancestry, that the possible origin of this word is from the Irish galic word for 'yes' (tá).
If you think of 'yes' in a broader context; and as and an affirmative response (i.e. Yes) to an action, it kinda makes sense.
Just my thoughts, any comments on this welcome.
english.stackexchange.com/users/None/
Where does the expression "ta" come from?  Wikipedia has only  this  to say:   "ta!", slang, Exclam. Thank you! {Informal}, an expression of gratitude   but no additional information or links about its genesis.  I have only ever heard it from englishmen and -women. Is it used anywhere else in the world? How did it come about? What is its history?
Where does "ta!" come from?
english.stackexchange.com
<expressions><history><linguistics>
english.stackexchange.com/questions/5567
english.stackexchange.com/users/239/Pekka
"Ta" is just a shortening of the word "thanks", though it may also be a mimic of the infantile word expressing thanks. It was first referenced in print in 1772 and is also used extensively in Australia. The OED denotes it as an infantile word used to express thanks.It is a short form of "thanks". It is used regionally to denote "thanks" in North England and in Australia for example .This may be due to inheriting the language from the Vikings.
"Ta" is just a shortening of the word "thanks", though it may also be a mimic of the infantile word expressing thanks. It was first referenced in print in 1772 and is also used extensively in Australia. It is  just a shortening of "thanks". The Oxford English Dictionary  lists it as "An infantile word expressing thanks," and dates its first reference from 1772. Although possibly originating from the imitative of baby talk, this is in widespread use in the North of England and Wales as an informal "thanks" amongst adults.    
The Oxford English Dictionary  lists it as "An infantile word expressing thanks," and dates its first reference from 1772. It is seen to be a shortened version of "thanks" and is used extensively. "Ta" is possible just a shortening of the word "thanks", though it may also be a mimic of the sound children make to express gratitude. It was first referenced in print in 1772 and is also used extensively in Australia.
The OED denotes it as an infantile word used to express thanks. It is a short form of "thanks" It is used regionally to denote "thanks" in North England and in Australia for example .This may be due to inheriting the language from the Vikings.
The Oxford English Dictionary  lists it as "An infantile word expressing thanks," and dates its first reference from 1772. Although possibly originating from the imitative of baby talk, this is in widespread use in the North of England and Wales as an informal "thanks" amongst adults.     It is  just a shortening of "thanks".
It is claimed that "ta" is a mimic of an infantil sound of gratitude and was first referenced in 1772. It is possibly just a shortening of the word "thanks". "Ta" is also used extensively in Australia.