The deal, first reported by ESPN, comes a year after the Nets offered Crabbe a four-year, $75 million deal as a restricted free agent. The Trail Blazers matched that offer.
A 6-foot-6 wing, Crabbe averaged 10.7 points, 2.9 rebounds and 1.2 assists last season in Portland. He hit 44.4 per cent of his 3-pointers.
"Allen has been a model teammate on the court and ambassador for the organization off the court," Blazers President of Basketball Operations Neil Olshey said in a statement. "He will be missed by all of us who shared the last four seasons with him."
Nicholson, who was traded from Washington to the Nets at the deadline in February, averaged 2.6 points and 1.6 rebounds last season. Portland is expected to waive the 6-foot-9 power forward.
Crabbe, 25, was the 31st pick in the 2013 draft by Cleveland but was immediately dealt to Portland. He was a former Pac-12 Player of the Year at California.
For his career in Portland, Crabbe averaged 8.3 points, 2.3 rebounds and 1.1 assists in 226 games, including 24 starts.
Nicholson, 27, was the 19th overall pick in the 2012 draft by Orlando. He played at St. Bonaventure.
By shedding Crabbe’s contract, the Blazers significantly lower their luxury tax penalty.