BBC News editor Deborah Turnes has also resigned along with Davy after criticism for misrepresenting Trump on Panorama.
"Like all public organisations, the BBC is not perfect and you must always be open, transparent and accountable," said Davie in a statement published on the BBC website.
"While the current debate surrounding BBC News is not the sole reason, it has understandably influenced my decision (...). I must take ultimate responsibility," Davies said in a statement.
A week ago, The Sunday Telegraph published a leaked internal memo that suggested Trump's remarks had been edited.
Earlier on Sunday, Minister for Culture, Media and Sport Lisa Nandy admitted that the allegations against the BBC were extremely serious.

%3Awatermark(https%3A%2F%2Ff.pmo.ee%2F%2Flogos%2F4132%2Fd583334e07b643b158b745b655f05032.png%2C-2p%2C-2p%2C0%2C18%2Cnone)%3Aformat(webp)%2Fnginx%2Fo%2F2025%2F11%2F09%2F17268849t1h3591.jpg&w=3840&q=75)