Lord Hall, who was heavily criticised in the Dyson report for his botched inquiry into how the interview was obtained, said his continued presence at the gallery would be “distraction”.
The report by former master of the rolls Lord Dyson found the internal BBC investigation had covered up the “deceitful behaviour” of reporter Martin Bashir.
In a statement Lord Hall, who was director of BBC news and current affairs at the time Bashir interviewed Diana, said: “I have today resigned as chair of the National Gallery.
“I have always had a strong sense of public service and it is clear my continuing in the role would be a distraction to an institution I care deeply about.
“As I said two days ago, I am very sorry for the events of 25 years ago and I believe leadership means taking responsibility.”