The sports presenter invested money into Icebreaker, a company which purported to support young musicians.
She said she chosen to invest in the scheme in “good faith” six years ago but pulled out of the investment two years ago.
Barlow and two other members of Take That are reportedly in line for tax bills totalling tens of millions of pounds after a court ruled that a partnership styled as a music industry investment scheme in which they invested was a tax avoidance scheme
Logan, who hails from Leeds and is part of the BBC’s World Cup team, said she invested “in good faith” after being told about the scheme in 2008.
It is not known how much money Logan invested into Icebreaker.
In a statement on her website, the BBC broadcaster said: “It was explained to me as a way of funding new acts in the music industry.
“Because of information which came to light in 2012, I decided the investment was not right for me.
“With new professional help and advisers, I have for some time been working to resolve the issue and I fully intend to pay any tax which should have been paid, had I not entered the business.”
She added: “I have been completely open and honest with HMRC and I have never hidden anything.”
Barlow, along with bandmates Howard Donald and Mark Owen and their manager Jonathan Wild, apparently invested £66m into two partnerships styled as music industry investment schemes.
Judge Colin Bishopp ruled that 51 partnerships, set up by Icebreaker Management, were to secure tax relief for members and HM Revenue and Customs is now expected to demand repayment of the cash.
It was alleged in 2012 that Take That’s frontman Barlow, Donald, Owen and their manager Wild invested at least £26m in a scheme run by Icebreaker Management.
At the time the chart-topping band’s lawyers insisted the band mates believed the investments were legitimate enterprises and that all four named paid “significant tax”.
The band, whose hits include Patience, Rule the World and Everything Changes, have enjoyed 54 international number one hits and have topped the UK albums charts seven times.
Prime Minister David Cameron has criticised the use of “aggressive” avoidance schemes but dismissed calls from some Tory and Labour MPs for Barlow to give up his OBE.
Mr Cameron said he did not think that removing the honour from Barlow was “necessary”.
Leeds-born Logan was last year installed as the new chancellor at Leeds Trinity University, in Horsforth.
The daughter of former Leeds United star Terry Yorath was a top gymnast but she was forced to retire from the sport when she was a teenager.
Logan then shot to fame as a broadcaster and some of her greatest achievements include being named as the first female presenter of a live football match and the first woman to host Match of the Day.
The mother-of-two is married to former Scotland rugby player Kenny Logan.