It comes after Diana's brother alleged that BBC journalist Martin Bashir used forged bank statements to convince her to do the Panorama interview in 1995.
Lord Dyson, one of the country's most senior retired judges, has been appointed to lead the inquiry.
A former Supreme Court judge, he retired in 2016.
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The BBC's director general, Tim Davie, said: "The BBC is determined to get to the truth about these events and that is why we have commissioned an independent investigation.
"Lord Dyson is an eminent and highly respected figure who will lead a thorough process."
Diana's brother, Earl Spencer, called for an independent inquiry earlier this month, saying "sheer dishonesty" was used to secure the interview with the princess.
In a letter to Mr Davie, reported by the Daily Mail,the earl said Bashir had used forged bank statements, which wrongly purported to show that two senior courtiers were being paid by the security services for information on his sister.
Earl Spencer wrote: "If it were not for me seeing these statements, I would not have introduced Bashir to my sister."
In another Daily Mail interview,he also alleged that the then Panorama reporter made a number of false and defamatory claims about senior royals during a meeting with him to gain his trust and access to his sister.
These claims included that Diana's private correspondence was being opened, her car tracked and phones tapped - described by the Mail as "preposterous lies".
Bashir, 57, currently BBC News religion editor, is recovering from heart surgery and complications from Covid-19 and has been unable to comment on Earl Spencer's allegations.
What will the investigation look at?
1. What steps did the BBC and, in particular, Martin Bashir take with a view to obtaining the Panorama interview in 1995? This will include looking at the mocked up bank statements, alleged payments to members of the royal household, and other issues raised by Earl Spencer.
2. Were those steps appropriate, particularly in regard to the BBC's editorial standards at the time?
3. To what extent did the actions of the BBC and, in particular, Martin Bashir influence Diana's decision to give an interview?
4. What knowledge did the BBC have in 1995 and 1996 of the relevant evidence, such as the forged bank statements?
5. How effectively did the BBC investigate the circumstances leading to the interview?
These terms of reference for the investigation were set by Lord Dyson and agreed by the BBC.
The BBC said the investigation would start straight away and it was handing over "all of its relevant records".
Last week, the broadcaster revealed that a previously missing note from Diana,thought to indicate she was happy with the way interview by BBC panaroma was obtained, had been found and would be handed over to the investigation.
Leading the inquiry will be Lord Dyson, who was Master of the Rolls - the second most senior judge in England and Wales - for four years until he retired in October 2016.
His other influential positions have included being a Justice of the UK's Supreme Court - the highest court in the country - and a Lord Justice of the Court of Appeal of England and Wales.
MP Julian Knight, chair of the Digital, Culture, Media and Sport Committee (DCMS), said the investigation was the right way to proceed "given the gravity of the subject".
He added: "The DCMS Committee has no plans to hold its own inquiry into this matter, however we will review the outcome and reserve a decision on whether any further action should be taken at that point."
Almost 23 million people tuned in to watch the Panorama programme 25 years ago.
In it, the princess famously said "there were three of us in this marriage", referring to the Prince of Wales's relationship with Camilla Parker-Bowles.
At the time, Princess Diana was separated from Prince Charles but not yet divorced. She died on 31 August 1997, aged 36, in a car crash in Paris.
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