The Sātavāhanas began as feudatories to the Mauryan Empire. They seem to have been under the control of Emperor Ashoka, who claims they were in his domain, and that he introduced Buddhism among them:
Here in the king's domain among the Yavanas (Greeks), the Kambojas, the Nabhakas, the Nabhapamkits, the Bhojas, the Pitinikas, the Andhras and the Palidas, everywhere people are following Beloved-of-the-Gods' instructions in Dhamma.
—Rock Edict Nb13 (S. Dhammika)
The Satavahanas declared independence sometime after the death of Ashoka (232 BCE), as the Maurya Empire began to weaken.
It is believed that they were originally Brahmins, practicing Hindu religion (as per Sthala Purana of Amaravathi. Some rulers like Maharaja Satakarni are believed to have performed Vedic sacrifices as well.
They were not only worshipers of Vishnu and Shiva but also respected Buddha, but also other incarnations of, Gauri, Indra, the sun and moon.They were mostly Buddhistic Vaishnavites. Under their reign, Buddha had been worshiped as a form of Vishnu in Amaravati