Impeccably dressed in a dark suit, Weil, who has pleaded not guilty, looked relaxed as his trial opened in federal court here with the selection of a 12-member jury.
Prosecutors allege that the 54-year-old Swiss citizen helped US clients conceal some $20 billion in assets from tax authorities between 2002 and 2007.
In his opening arguments, Mark Daly, an attorney with the tax division at the Justice Department, called the case "classic, simple tax fraud."
Weill's motive, Daly said, was plain, old-fashioned greed.
"He had the power to shut this business down," the prosecutor said, but failed to do so, "because UBS was making too much money."
At the time, Weil headed UBS's global wealth management business, supervising overseas activities that served some 20,000 customers.
He was charged in 2008 with conspiracy to commit tax fraud as part of a massive US crackdown on offshore tax dodging, particularly in Switzerland, renowned for its vault-like banking secrecy.
Federal Judge James Cohn said he expects the trial to last four weeks.
Prosecutors plan to call as witnesses former bankers who have agreed to testify in return for clemency in their own cases.
Weil's attorneys, for their part, intend to call 10 witnesses, two or three who will testify via videoconference from London because they fear arrest if they set foot on US soil.
The defence was expected to make its opening arguments later Tuesday.
Weil, who was extradited to the United States after being arrested in Italy in 2013, contends the tax evasion was the work of other UBS employees, acting without his knowledge.
Weil maintains innocence
Aaron Marcu, Weil's attorney, insisted in court that his client did nothing wrong.
"Weil did not agree with anyone to defraud the IRS," he said, pinning blame instead on "a small group of Swiss bankers."
Speaking to AFP earlier, the defence attorney pointed the finger at "the same people at UBS who were doing bad things and helping clients hiding assets are the same who are going to testify against him."
Weil has been living in New Jersey after being freed on $10.5 million bail last December.
He was ordered to surrender his passport and wear a GPS tracking monitor.
Fired by UBS in April 2009, Weil joined the wealth management firm Reuss Private Group in 2010 as a consultant, then became head of the company in early 2013.
That career came to an end when he was arrested in October 2013 after using his real name to check into a luxury hotel in Bologna, Italy and he was extradited to the United States.
UBS has been cooperating with US authorities under an agreement reached in February 2009 that resulted in a $780 million fine.
The bank has turned over the names of many of its US clients suspected of tax fraud.
If convicted, Weil could be sentenced to five years in prison.