Mr Justice Rattee said Kenneth Martin had brought disaster upon himself by failing to comply with court orders requiring him to provide the Band Aid trustees with details of his accounts from the time when he acted as the charity's shipping agent.
Mr Martin denied the allegations levelled against him by the charity's trustees, including the musicians Bob Geldof and Midge Ure; Channel 4's chief excutive, Michael Grade; and the promoter Harvey Goldsmith.
But, for his failure to comply with court orders, Mr Justice Rattee "debarred" him from defending the action.
The judge said the damages award was said by the charity to be "a conservative estimate" of what it had lost "given the paucity of information" provided by Mr Martin.
Band Aid's counsel, Ms Monica Carss-Frisk, claimed that Mr Martin had, in April 1985, agreed to ship the charity's famine relief supplies to Ethiopia and Sudan on condition that he was indemnified against all his costs.
In February 1986, Mr Martin had also undertaken to purchase relief supplies on Band Aid's behalf, she alleged.
Mr Justice Rattee said it was the charity's case that Mr Martin had "overcharged" it for the chartering of cargo ships, for a shipment of wheat purchased by him on the trust's behalf, and for port and fuel costs.
It was also alleged Mr Martin had used vessels chartered for Band Aid to carry his own "non-charitable" cargoes before charging the charity for his own costs.
Mr Martin was also claimed to have failed to comply with his undertaking to the charity to provide full accounts and access to records of transactions carried out on its behalf, the judge said.
Ms Carss-Frisk said Band Aid was claiming £1,241,000 damages from Mr Martin with interest of £1,239,922.22.
"This is very much the tip of the iceberg. The claim we are making is a very conservative one. We are, in all likelihood, entitled to much more," she said. She alleged vessels chartered by Mr Martin on Band Aid's behalf had made "fifty unexplained stops"on their relief trips.
Had he not been debarred from defending the action, Mr Martin would have denied entering into any agreements with Band Aid and would have claimed that he was himself owed £700,000.
The judge ordered Mr Martin, of The Willows, Byrants Lane, Woodham Mortimer, Essex, to pay damages inclusive of interest totalling £2,481,026.22 to the charity.
He was also ordered to pay the legal costs of the action, which began in 1989.