Portland will receive forward Andrew Nicholson in the exchange. The teams announced the transaction Tuesday afternoon.
Crabbe, 25, averaged a career-high 10.7 points 2.9 rebounds and 1.2 assists in 79 games last season. The second round pick in the 2013 NBA Draft has played his first four NBA seasons for the Trail Blazers.
Brooklyn gave Crabbe an offer sheet worth about $75 million over four years last offseason, but the Blazers decided to match and retain the guard. The move saves the Blazers $43.9 million in luxury tax penalties, according to The Ringer. Portland's luxury tax penalty drops from $48.3 million to $4.4 million after the move.
Crabbe also waived his $5.6 million trade kicker in the deal.
Nicholson signed a four-year, $26 million contract last offseason with the Washington Wizards. The 27-year-old was the No. 19 overall pick in the 2012 NBA Draft. He played his first four seasons with the Orlando Magic before joining the Wizards in a February trade.
Nicholson averaged 3.0 points and 2.7 rebounds per game in 10 appearances last season for the Nets.
Crabbe had an $18.5 million salary last season and is due $19.3 million in 2017. The sharpshooter hit 44 percent of his 3-pointers last season and owns a career 41 percent shooting clip from downtown.
The shooting guard joins D'Angelo Russell and Jeremy Lin in the Nets' backcourt. In addition to Russell and Crabbe, the Nets have also added Timofey Mozgov and Marcus Thornton this offseason via trade.