Nets coach Avery Johnson confirmed Thursday that the sharpshooting Williams has chosen New Jersey over the Knicks.
The deal is reportedly for two years and $6.1 million.
"He gives us a guy that can stretch the floor," Nets general manager Billy King said of Williams, who shot 40.1 percent from 3-point range for the Knicks last season. "We were looking at that as we tried to build a team."
Outlaw -- who averaged 9.2 points and shot 38 percent from the field last season -- has four years and $28 million remaining on his contract. The Nets will still have to pay it, but through the amnesty provision they receive salary cap relief by waiving Outlaw.
"I told Travis, it's part of the business. It's the ability to have flexibility," King said. "It has nothing to do with you. I've got to keep as much flexibility for the organization as possible."
Williams, 25, played in 64 games for the Knicks last season, averaging 7.1 points per game on 40.1 percent shooting from 3-point range.
A four-year pro, Williams holds career averages of 5.9 points and 2.9 rebounds per game.
His departure leaves a void on the Knicks' bench. Williams knocked down a career-high 40 percent of his 3-point attempts last season and was a versatile defender.
"Shawne worked really hard last year to get in this position right here so he deserves it," Knicks forward Carmelo Anthony said. "I wish him all the luck. I miss him as a teammate. But he's got to do what he has to do."
Added Amare Stoudemire: "Shawne made a decision that's best for him and his family as far as I'm concerned. We have a solid team with what we have ... so best of luck to him. We'll see him shortly."
The Knicks and Nets play the first of two preseason games on Saturday at the Prudential Center in Newark.
Williams was actually traded to the Nets along with Kris Humphries from Dallas in exchange for Eduardo Najera on Jan. 11, 2010. But they waived Williams four days later after he'd been arrested and later pleaded guilty to charges of drug possession. He's also had other issues with the law, which include a previous arrest on charges of drug possession and driving with a suspended license.
Point guard Deron Williams was involved in discussions with Nets' brass to bring in the 6-foot-9, 250-pound Shawne Williams.
"I like having shooters around me," Deron Williams said. "It's always a positive. He's a good pickup for us."
The Nets also love Shawne Williams' versatility. He could also play a stretch power forward position if need be.
Now they'll turn their attention to addressing their need at power forward. Re-signing Humphries could be an option, as may bringing in Deron Williams' former teammate in Utah, Andrei Kirilenko.
"There's not many guys that can fill up a stat sheet like he can across the board," Williams said of AK-47. "He's a versatile player. I think he just took a lot of negative publicity from the size of his contract in Utah, but he was still a great player for us. ... For the right price, he's a bargain."
Williams downplayed the recent news that the Orlando Magic had taken superstar Dwight Howard off the trade market. The Nets were heavily interested in acquiring Howard, but they couldn't meet Orlando ownership's demands.
King would not address the Howard situation, saying he doesn't speak about trade rumors.
Mike Mazzeo is a regular contributor to ESPNNewYork.com. Information from ESPNNewYork.com's Ian Begley was used in this report.