The agreement came 10 days before jury selection was scheduled to begin in one of three cases.
The Low case included Trump University students in California, New York and Florida, who sued Trump in 2010 over claims he defrauded them when they invested up to $35,000 to learn insider real estate secrets from instructors purportedly handpicked by Trump.
The presiding judge is Gonzalo Curiel.
His attorneys have also raised the prospect of having him testify by video recording before the trial begins in the class-action lawsuit on November 28.
The settlement lifts what would probably have been a major headache for Trump as he works to fill key executive branch positions and get acquainted with foreign leaders.
The $25 million settlement will cover all three cases in California and NY and will be made public.
Trump's political rivals seized on the lawsuits to try to portray him as dishonest and deceitful. Trump suggested the Indiana-born judge's Mexican heritage exposed a bias.
A spokesperson for New York Attorney General Eric Schneiderman said the attorney general "has always been open to a settlement that fairly compensates the many victims of Trump University who have been waiting years for a resolution".
Trump attorneys to argue for delay in Trump University trial
Class attorney Jason Forge. Trump denies the allegations and has argued he relied on others to manage the business. I don't believe in it. "I already am, as far as I'm concerned", Trump said in June, according to the BBC.
The deal doesn't require Trump to acknowledge wrongdoing.
Since the election, Trump's attorneys had been scrambling to get the trial postponed until after Trump's January 20 inauguration - citing the "momentous task" of assembling a cabinet and preparing for the presidency. Petrocelli said he would talk to Trump about that possibility. "Today, that all changes".
Trump's attorneys said in a court filing last week that preparations for the White House were "critical and all-consuming". They also proposed that Trump's trial testimony be recorded before trial.
Real estate mogul Donald Trump (R) speaks as university president Michael Sexton (L) looks on during a news conference announcing the establishment of Trump University May 23, 2005 in New York City. People will be bringing that emotion into court, and the question is whether they can put it aside'.
Trump has repeatedly claimed a 98 percent customer satisfaction rate on internal surveys.
The settlement comes a day after watchdog groups and ethics experts who served in both Republican and Democratic administrations sent a letter to Trump urging him to make a clean break from his business to avoid "embroiling the presidency in litigation". He called the talks "surprisingly cordial" and said the attorneys worked on the settlement "up until an hour" before Friday's hearing.
"He has very, very strong feelings about this case", Petrocelli said at the time.