It's called the "ta-da" sting because it has exactly the same rhythm, melody and inflection as the phrase "Ta-da!" which is used commonly when a person produces something, as if by magic. That's the easy part of the question.
The harder question is "why." The standard explanation is that the phrase is a vocal imitation of a ...
The Stereolab newsletter, The Lab Report, 25 March 2019 states the sample was from George Harrison's "Wonderwall".
I have not been able to locate a copy of "Pack Yr Romantic Mind" containing this sample that is available for purchase.