Swiss attorney Cornel Borbely has succeeded Michael Garcia, who quit in protest in December.
Garcia was unhappy at how Fifa officials handled his investigation into the bidding process for the 2018 and 2022 World Cups.
Borbely said: "I don't take any orders at all from Fifa, none whatsoever."
The 36-year-old, who was Garcia's deputy, told Reuters: "I alone decide whether to open, conduct and conclude an investigation.
"I am completely independent of any Fifa officials, otherwise I couldn't, and wouldn't, do this job. Nobody interferes, neither the Fifa executive committee nor anybody else."
Borbely headed an economic crimes investigation unit in Zurich for three years and has worked as a prosecutor for a military tribunal.
He said anyone coming forward with information about alleged Fifa corruption could do so in confidence, with any tips "carefully evaluated".
The Swiss added: "I also have my eyes and ears open and if I see something that calls for it, of course I open a preliminary investigation."
Fifa has suffered a series of damaging allegations in recent years, including claims of corruption in the bidding process for the 2018 and 2022 World Cups, which were awarded to Russia and Qatar respectively.
US lawyer Garcia was called in to investigate those allegations and produced a 430-page report last year.
However, when a 42-page summary of his findings was published, which claimed there had been no wrongdoing, Garcia complained to Fifa about its "erroneous" representation of his work.
Fifa dismissed his appeal, prompting his resignation, but has since agreed to release a redacted version of Garcia's full 430-page report.
Fifa's new independent ethics chief says "nobody will interfere" with his task of keeping corruption out of football's world governing body.