Weiss will plead guilty to "limited participation in a criminal conspiracy" involving payments to plaintiffs, attorney Benjamin Brafman said in a statement.
"I deeply regret my conduct and apologize to all those who have been affected," Weiss said in the statement.
Brafman did not specify the charges involved in the plea. Weiss previously pleaded not guilty to one count each of conspiracy, mail fraud, money laundering and obstruction of justice in a revised indictment.
The plea deal calls for Weiss to receive a prison sentence of 18 to 33 months, with the court able to substitute time in home confinement or community service.
Weiss also agreed to pay $10 million in fines and forfeiture penalties, according to the statement.
Authorities say the firm now known as Milberg Weiss made an estimated $250 million over two decades by filing legal actions on behalf of professional plaintiffs who received $11.3 million in kickbacks.
The lawsuits targeted companies such as AT&T, Lucent, WorldCom, Microsoft Corp. and Prudential Insurance.