The Real Academia Española (RAE) allows both terms. Both words may be used interchangeably, but the authors of the "Diccionario de la Real Academia Española" give preference to "brasileño" form.
Interestingly, countries near Brazil (Argentina, Paraguay, Uruguay, Peru, Bolivia) interchangeably use both forms "brasileño" and "brasilero", the latter being an adaptation of the original adjective in Portuguese: "brasileiro".
In other countries (Spain, Mexico, Cuba) it is more common to use the form "brasileño".
Tip # 16
:: tip #