The transaction will not become official until Feb. 9, the first day NFL teams can make waiver requests.
"He was surprised, and I think he was obviously somewhat hurt," said Worrick Robinson, Jones' agent. "At the same time, he understands the business behind what is happening here."
The Cowboys traded for Jones before the season even though he had been suspended in 2007 because of a series of off-field incidents.
He missed six games this season for violating the league's player conduct policy after an Oct. 7 scuffle with a team bodyguard at a Dallas hotel. He missed a seventh game with an injury.
Jones averaged just 4.6 yards per punt return and had no interceptions.
Robinson said he did not think Jones' suspension was a factor in the Cowboys' decision to release the cornerback.
"We don't have any reason to believe at this point that that off-the-field incident had anything to do with the team's decision today," Robinson said. "I know there was certainly a lot of bad that came out of that situation, but there was some good that came out of that situation as well."
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