The Wizards dealt forward Quinton Ross to the Nets, who also sent an undisclosed amount of cash to Washington.
The Nets freed up another $3 million with the deal, leaving them about $30 million to spend once free agency opens on July 1.
It was the second time in less than a week the Wizards helped a team in the LeBron James chase. The Chicago Bulls added to their cap space on draft night when they traded guard Kirk Hinrich to Washington.
"I think we're concerned about our own situation, and this fits in with our plan of adding young players, players that can part of a core going forward," Wizards president Ernie Grunfeld said. "We've got a player who's had success in the NBA and at the same time is only 22 years old."
Yi was the No. 6 pick in the 2007 draft by Milwaukee and has now been traded twice. He averaged career highs of 12.0 points and 7.0 rebounds last season, but was limited to 51 games because of injury.
The forward from China, scheduled to earn $4.1 million next season, has averaged 9.6 points and 5.8 rebounds in his career. The Wizards used a trade exception to complete the deal, again bringing in a player when many teams have preferred financial flexibility ahead of free agency.
"We made a decision that we're going to save some of our powder for the future and try to right now put a core of young players together that can grow and we can build with, and that is the reason that we do have those opportunities right now," Grunfeld said. "Otherwise, they probably wouldn't be there for us."
New Jersey may have found Yi's replacement when it drafted Derrick Favors from Georgia Tech with the No. 3 pick, or could target another power forward in free agency.
Ross spent last season with Dallas and Washington, and also has played for the Clippers and Memphis Grizzlies in his six-year career. He holds career averages of 4.3 points and 2.2 rebounds.
AP Sports Writer Joseph White in Washington contributed to this report.