He has previously claimed he was shown "false bank statements" by interviewer Mr Bashir ahead of Diana's interview with Panorama.
The statement was released on Twitter by royal author and correspondent Omid Scobie.
"The independent investigation is a step in the right direction", William said in a statement.
As the edition writes People, the objective of the investigation is to understand the circumstances under which the journalist Martin Bashir in 1995 took the famous scandalous interview with Princess Diana, who frankly talked about how unhappy she was in marriage, about adultery and her depression. In 2005, Charles married Camilla, now the Duchess of Cornwall.
"The BBC is determined to get to the truth about these events and that is why we have commissioned an independent investigation", said Tim Davie, BBC director-general, adding that Dyson "is an eminent and highly respected figure who will lead a thorough process".
Spencer alleged that in the weeks leading to the 1995 interview, Bashir made false and defamatory claims about senior royals in order to gain his trust and access to his sister.
In the bombshell interview, viewed by a record of 22.8 million people, Diana talked in detail about her collapsing marriage with Prince Charles.
The investigation will be led by a former Supreme Court justice, the BBC said in a statement on Wednesday, and will focus on how the broadcaster obtained the interview and whether executives covered up any wrongdoing.
The Princess died in a Paris auto crash in 1997 as she was pursued by members of the paparazzi.
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"However, we think it is essential that the BBC ensures that the concerns raised about this programme are investigated thoroughly", it said in a letter to the broadcaster.
It will also look at revelations made by Spencer this month about Bashir to the Daily Mail, which said the reporter made "lurid claims" about Queen Elizabeth II, Charles and other royals.
Last week, The Sun exclusively revealed the BBC has found a note handwritten by Diana after the interview in which she reportedly denied being manipulated into taking part. These bank statements were allegedly used as proof that someone was leaking information about their family in exchange for money.
These claims included that Diana's private correspondence was being opened, her vehicle tracked and phones tapped - described by the Mail as "preposterous lies".
Diana also questioned Charles's suitability as king.
According to Reuters, Bashir has not publicly commented to the press and the BBC said he is on sick leave from his position as religion editor.
An internal investigation by the BBC after the original broadcast concluded that Bashir did not coerce Diana into giving the interview.