The authorities say James Richard Nolan and Adam Quinn are directors of the firm Process and Industrial Developments (P & ID).
The company won an arbitration award against the Nigerian government over a gas project that failed which is now worth $9bn (£7bn).
A lawyer representing Mr Nolan and Mr Quinn entered a not guilty plea to the money laundering charges put forward by the EFCC.
Mr Quinn is at large but Mr Nolan has been remanded in prison until his application for bail is considered.
In a statement, the EFCC said P&ID had failed to report a deposit of $125,000 in a local account.
The agency also says the company did not declare its activities in Nigeria to the trade ministry.
This is the latest development in a protracted battle between the British Virgin Islands-based firm and the Nigerian government, over an aborted gas deal dating back to 2010.
P&ID claims the failure of successive administrations to deliver their end of the deal, led it to suffer massive losses.
The Nigerian government says the deal was designed to fail and that the arbitration award was unfair.