Trump is accused of orchestrating a payment of $130,000 (£104,000) to porn actress Stormy Daniels 12 days before the 2016 presidential election, which he won.
Mr Bragg said: "Each cheque was processed by the Trump Organization and illegally disguised as a payment for legal services.".
And Trump has acknowledged reimbursing him for the payment, with the Trump Organization logging the reimbursement as legal expenses.
Please use Chrome browser for a more accessible video player 1:18 Trump leaves New York following hearing.
Trump was earlier formally arrested following his arrival at Manhattan Criminal Courthouse.
Image: Trump did a fist pump outside Trump Tower as he left for the courthouse.
Trump earlier pumped his fist as he left his nearby home at Trump Tower before being escorted to the courthouse in a motorcade by his Secret Service protection team. »