He was arrested on 2 November by HM Revenue and Customs, reports The BBC.
HMRC did not confirm the identity of the “49-year-old businessman”, but Mr Chappell told ITV News he had been arrested.
The tax related to the profits he made from the department store chain before it collapsed.
Mr Chappell’s company, Swiss Rock, was paid at least £1.6m by BHS following his controversial purchase of BHS from Sir Philip Green.
The Guardian reported that Swiss Rock owed £365,000 in VAT and £196,306 in corporation tax.
Speaking about Swiss Rock’s tax bill in September, Mr Chappell told the paper: “There was a return that was made in error; they [HMRC] have acted upon it and we are rectifying that as we speak.”
HMRC began legal action against Mr Chappell to recover the sums, but he has put Swiss Rock into liquidation, making it more difficult for the tax man to obtain the funds.
He took a total of £2.6m out of BHS, including a £600,000 salary, which he described as a “drip in the ocean” to the BBC in August.
“Did I take a lot of money out? Yes I did. But did the business fail because of the amount of money I took out? No it didn’t,” Mr Chappell said.
“This was just a drip in the ocean compared to the money that was needed to turn around BHS.”
The loss-making chain was bought by Mr Chappell last year. It went into administration in April and the last stores closed in August, with the loss of about 11,000 jobs and leaving a pensions deficit of hundreds of millions of pounds.
Last month MPs backed a call to strip Sir Philip of his knighthood for his role in the collapse of BHS.
The Pensions Regulator has started legal action against Sir Philip, his family’s companies and Mr Chappell after failing to reach a deal over the BHS pension fund deficit.
