Weiss, 72, also will acknowledge that he and others concealed secret payment arrangements that his firm, Milberg Weiss, had with named plaintiffs in the lawsuits, prosecutors said in a statement.
Under a plea deal, he could be sentenced to up to 33 months in prison and pay $10 million.
His firm dominated the industry in securities class-action lawsuits, which involve shareholders who claim they suffered losses because executives misled them about a company's financial condition.
Authorities said the firm made an estimated $250 million over two decades by filing legal actions on behalf of professional plaintiffs who received $11.3 million in kickbacks.
Weiss' plea deal was confirmed by attorney Benjamin Brafman, who represents Weiss.
Brafman did not specify the charges involved in the plea but said in a statement his client would admit "limited participation in a criminal conspiracy" involving payments to plaintiffs.