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That will leave G. Mike Mikan, who was named interim CEO when Dunn abruptly resigned amid a probe into allegations of personal misconduct, in charge of the world's largest consumer electronics retailer for some time as it struggles in a competitive and changing sales environment.
The Minneapolis Star Tribune and other media reported on Thursday that Best Buy's audit committee is investigating whether Dunn used company resources to carry on an inappropriate relationship with a female staffer.
Dunn has not responded to several attempts from Reuters this week requesting comment on the probe.
Greg Hitt, an outside spokesman for Best Buy's board, declined to comment on details of the board's investigation or the media reports.
Best Buy is creating a committee to run the search for a new CEO, the company said in a statement on Thursday evening.
The committee will be headed by Kathy J. Higgins Victor, a board member and chairwoman of Best Buy's nominating committee, the retailer said.
Six to nine months seemed like a long time particularly given the rapid pace of change in the consumer electronics retailing industry, BB&T Capital Markets analyst Anthony Chukumba said.
Still, he did not think it was necessarily a bad idea.
I think that the board wants to be very deliberate about this, very thoughtful about this. This really is an inflection point for Best Buy. So I would rather have them take their time, vet all the candidates, extensively interview them, figure out what their visions are, and then pick the right person, Chukumba said.
In late March, Best Buy announced plans to close 50 of its 1,100 large U.S. stores and cut 400 jobs, disappointing investors looking for even deeper cuts to turn around the chain.
Best Buy is now trying to move away from the big box business model and focus on smaller stores that will sell mobile phones. It is also testing remodeled store formats in San Antonio and Minneapolis.
The newly-formed committee will oversee a thorough search process to identify internal and external candidates, including Mikan, Best Buy said on Thursday.
Charles Elson, professor of finance/legal studies at the University of Delaware who is an authority on corporate governance issues, said six to nine months was about the right amount of time to do a thorough and careful search for a new chief executive.
I don't think it's out of the ordinary. I've seen them longer, said Elson.
Dunn, who started at Best Buy as a sales associate in 1985 and rose through the ranks to become CEO in June 2009, resigned abruptly this week from the world's largest consumer electronics chain during a company probe into allegations of personal misconduct.
Also on Thursday, a source familiar with the matter told Reuters that law firm WilmerHale was helping Best Buy's audit committee to conduct the investigation on Dunn.
(Additional reporting By Martinne Geller; Editing by Bernard Orr)