Mr Hall said such an incident “must never happen again” and assured her the BBC had a “proud record” of supporting women’s sport, as well as working hard to ensure respect in the workplace.
It followed a robust letter he received from Mrs Miller in which she attacked sexist sports coverage and asked to be kept informed about any further action which would be taken over Inverdale’s comments on BBC Radio 5 Live.
More than 600 people complained about the sports broadcaster when he said Wimbledon winner Marion Bartoli was “never going to be a looker”, ahead of the women’s singles final.
In his response, Mr Hall said: “I agree that the comments made by John during the build-up to the Women’s Final were totally unacceptable and fell well beneath the standards we expect of our presenters.
“John sincerely regrets that he made such an inappropriate statement and for the offence caused. As he said on-air the following day, he has written to Marion Bartoli to apologise and the BBC has also apologised for John’s remarks.
“In addition, the director of sport and the controller of 5 live have both spoken to John to make it clear that his comments were unacceptable and that an incident of this nature must never happen again.”
Mrs Miller was moved to write her letter over the “derogatory” way Bartoli was treated during Wimbledon.
She wrote: “It is ... a matter of some concern to me that any comment on the looks and stature of a female athlete could be made in the context of one of the highlights of the UK’s, and indeed the world’s, sporting calendar.
“I am sure you will agree with me that it is vital that young women and girls in this country feel motivated both to take part in and to watch coverage of sport, and to know that they are included in the enjoyment of sport, and catered for by the media just as much as the male audience.”
She is understood to have met broadcasters a number of times to encourage them to improve coverage of women’s sports.
Mr Hall’s letter went on: “The BBC has a proud record of supporting women’s sport, as I am sure you will have recognised from the current coverage of Euro 2013.
“We are building on the fantastic success of the Olympics, with a team including many women broadcasters, through extensive day-in-day-out coverage across our TV, radio and online services. With the tennis at Eastbourne (and, of course, Laura Robson’s inspiring efforts at Wimbledon), the Women’s British Open Golf Championship, as well as the Anniversary Games and the World Athletics Championships...there is unprecedented coverage of women’s sport across the BBC this summer. “