A Brazilian Butt Lift involves harvesting fat from an unwanted area and then preparing it for transfer where it is injected into the buttocks as a living transplant. As long as you maintain your body at a stable level, the results should be permanent. Implants are also another permanent option but this procedure is riskier and involves a longer recovery time.
Please remember that not all fat survives but that which does will continue to live. Also the native buttock fat (but not so much the transplanted fat) will continue to atrophy and disappear with time.