The wide receiver told the newspaper that Jones said the move was being made for salary-cap reasons.
"It is a business. It is what it is," Williams said. "It's a business. I would have done the same thing."
The decision will end Williams' disappointing 2½-season Cowboys tenure that began in the middle of 2008, when Dallas traded away four draft picks -- including a 2009 first-rounder -- to acquire the receiver. Williams signed a five-year extension worth $45 million, including more than $20 million guaranteed, on the day of the trade, but he never quite lived up to expectations. He hauled in 94 catches for 1,324 yards and 13 touchdowns in 40 games with the team.
The Star-Telegram reported that Williams was scheduled to make $5.1 million in base salary and would have counted $9.5 million against the cap.
Williams expressed regret for the way his time in Dallas turned out.
Right guard Leonard Davis was told he will be released once teams are allowed to do so, a person familiar with the decision told The Associated Press on condition of anonymity because the team hadn't made an announcement. Right tackle Marc Colombo said he was told that he, too, could be gone.
Running back Marion Barber came and went from team headquarters within an hour, and he likely also received a farewell from Jones. Barber honked twice as he left in his car, but he didn't stop to speak with reporters.
Jones arrived at team headquarters about 40 minutes before the official start of the post-lockout flurry of activity and proclaimed that he would clear enough space under the salary cap to sign anyone he wants. He added that, "Before the day is over, we will have contact with any player we have an interest in."
Part of the money being cleared is to re-sign left tackle Doug Free. A four-year veteran, Free went from a restricted free agent to unrestricted under the terms of the lockout.
Dallas also spent its top draft pick on Tyron Smith. He was expected to replace Colombo at right tackle but could be forced to the left side if Free gets away.
Free was among the first players at team headquarters, perhaps so Jones could tell him he's the team's top priority.
Colombo said he expected to find out whether or not he's sticking around "in the next day or so."
"My goal is to play here," said Colombo, who was among the veterans who helped run offseason practices. "If it doesn't (happen), it's been a great six years here with the Dallas Cowboys and I appreciate it."
The Associated Press contributed to this report.