Brent was involved in a car wreck in December in which practice squad linebacker Jerry Brown was killed. Brent's blood alcohol level was 0.18, more than twice the legal limit in Texas.
"This is the right decision for me, and something that I have given a lot of thought to. I am at a point where my main focus is all about getting the priorities in my life in order," Brent said in a statement.
"Those priorities are more important than football. Doing the right things in life are more important than football. I love the game very much. I love my teammates, but this is the right thing for me to do."
Brent, 25, has a Sept. 23 court date, and his attorneys have spoken with the district attorney's office about a plea agreement.
"I think, in my mind, it speaks for itself," Cowboys owner Jerry Jones told ESPNDallas.com. "He wants to concentrate on where he should be concentrating on in his life. This allows him, in my mind, to do that."
Jones visited with Brent for 20 minutes regarding his decision. Jones said he didn't want to speculate regarding a Brent return and said the player is part of the football family.
"He's certainly got the ability to play," Jones said. "Let's focus on where it's got to be focused, and that's him getting his life in order, off the field and this is what this does. He wants to."
Cowboys coach Jason Garrett said it was premature to think about a Brent return.
"Josh, as he said in his statement, believes he needs to get his life in order," Garrett said. "Football is very important to a lot of us. It's important to Josh. But there are other things that are more important, and that's what he needs to do right now for himself and it's a good decision. He has to take it one day at a time and get himself going and get his life back together."
The Cowboys placed Brent on the non-injury reserve list after the accident but didn't release him because of a promise the franchise made to Brown's mother, Stacey Jackson.
"I've forgiven him," Jackson told WFAA-TV in Dallas. "Because he has enough on his plate with just reliving the whole thing over and over, and that's going to be for the rest of his life."
In the offseason, Brent failed two court-ordered drug tests for marijuana and spent a week in jail after his bond was rescinded by a Dallas County judge.
Brent also went to court when his alcohol-monitoring device went off several times. A judge didn't revoke his bond but instead added another device that monitored what Brent did.
Garrett said he didn't speak to Brent about his retirement.
"He's a great young man who made a mistake and he wants to get his life back together again," Garrett said. "We're there to support him and help him in any way that we could, and he thinks this is the right decision for him to help him get back as quickly as possible."
Brent's agent, Peter Schaffer, said Brent "made a very mature decision to put his priorities in order. I'm very proud of him."
NFL spokesman Greg Aiello indicated the league would not punish Brent now that he is stepping away from football.
"With his retirement, there is no action for us to take at this point," Aiello said.
Any request for reinstatement by a retired player must be reviewed and approved by the league, Aiello told ESPNDallas.com.
One of Brent's attorneys, George Milner, said the retirement has no effect on the criminal case.
In the 2012 season, Brent finished with 22 total tackles, 1.5 sacks and one forced fumble. Taken by the Cowboys in the seventh round of the 2010 supplemental draft, Brent played three seasons for the Cowboys, recording 65 tackles, 1.5 sacks and one forced fumble in 39 games with five starts.
The Cowboys report to training camp this weekend.
ESPNDallas.com's Calvin Watkins and ESPN NFL Insider Adam Schefter contributed to this report. Information from The Associated Press also was used.