There are different stories about its origin, and here you go:
The Gods & Goddesses pleaded Lord Brahma to create another veda which would be simple for the common man to understand. It is believed that considering this request Lord Brahma created the Panchamaveda , Fifth veda, Natyaveda , an essence of the other four vedas. It is believed that he has taken pathya (words) form the Rigveda, abhinaya (gesture) from the Yajurveda, get (music and chant) from Samaveda and rasa (sentiment and emotional element) from Atharvaveda to form the fifth veda, Natyaveda.
After creating this natyaveda, Lord Brahma gave the same to sage Bharata and asked him to popularize this veda on earth. Following the words of Lord Brahma, sage Bharata wrote Natyashastra or the Science of Dramaturgy, a great, comprehensive work on the science and technique of Indian drama, dance and music. Bharatanatyam might have got its name from sage Bharata also.The dancers still follow this work to perform.
There is also another story which says that Goddess Parvathi taught this dance form to Usha, daughter of Banasura, a demon. Usha taught the same to the Gopikas of the city of Dwaraka, Lord Krishna's birth place. Thus the divine dance form Bharatanatyam was introduced to the mankind.
Praveen & Virginia, a couple who believe in this great ancient Indian Arts - Yoga & Dance, and would love to share to everyone.