Mr Vance and Ms James attended Thursday's arraignment.
"This investigation will continue, and we will follow the facts and the law wherever they may lead," Ms James, who had been conducting a related civil probe, said in a statement.
Weisselberg wore handcuffs as he was led to the courtroom, and after being released was driven away in a black SUV. "You're going to prison," an onlooker shouted.
"He will fight these charges in court," Weisselberg's lawyers Mary Mulligan and Bryan Skarlatos said in a joint statement before the charges were announced.
Mr Alan Futerfas, a lawyer for the Trump Organisation, told reporters that the company was "very optimistic" the charges would not significantly hurt its business.