Charlie Shrem from BitInstant.com admitted the charges in a New York federal court hearing.
Another Bitcoin trader, Robert Faiella, also pleaded guilty.
Both were arrested in January, accused of selling more than $1m (?603,000) in bitcoins to users of online drug marketplace the Silk Road.
The site was shut down last year and its alleged owner was arrested.
The two traders admitted the charges as part of a deal struck with US prosecutors in order to settle the allegations against them.
Bitcoin exchanges are services that allow users to trade bitcoins for traditional currencies.
Mr Shrem had been accused of allowing Mr Faiella to use BitInstant to purchase large quantities of bitcoins to sell on to Silk Road users who wanted to buy drugs anonymously.
The authorities said Mr Shrem was aware that the bitcoins were being used for such purchases, and therefore he was in violation of the Bank Secrecy Act.
The Act requires financial institutions in the US to alert authorities to any suspicious activity that may suggest money laundering is taking place.