The chief legend of Godavari Tir Shakti Peeth relates to the creation of the Shakti Peethas. Sati, the daughter of Prajapati Daksha, was married to the god Shiva versus his wishes. Daksha arranged a great yajna but did not invite Sati and also Shiva. Uninvited, Sati reached the yajna-site, where Daksha ignored Sati as well as Shiva.
Sati was not able to withstand this insult. So, Devi Sati gave her life by jumping into the fire of Havan organized by her father King Daksh. When Lord Shiva was running around the planet carrying her body that Lord Vishnu divided the body into 51 parts utilizing his Sudarshan chakra. Out of those 51 parts, from which the ‘left Cheek’ of Sati fell to this place.
There is one puranic reference about Sage Gautama who lived on the Brahmagiri mountains at Trayambakeshwar with his wife Ahalya. Sage Gautama, when attempted to repel a cow which ate all the stock of rice in his granary. As the sage was going after the cow with Durbha grass, the cow fell dead. The sage practiced meditation upon Lord Shiva and desired to rid himself of the Gohatya. (Act of killing the cow).
He desired Lord Shiva to bring the Ganges to cleanse his hermitage. Lord Shiva was satisfied with the worship of Sage Gautama and appeared as Triambaka and brought down River Ganges to Trayambakeshwar. The river is also called Gautami, as it was brought down by Sage Gautama. The river gets the name Godavari, as the river was brought down to absolve Sage Gautama from the sins of “Gohatya”.
When this temple was constructed, there is no specific info about who and. It is stated and also written in Puranas and Vedas that the left Cheek of Maa Sati fell. In order to embark significance to this place and wish the Maa Sati, this Godavari tir Shakti Peeth temple was built.