The trade has been submitted for league approval, sources told ESPN The Magazine's Chris Broussard.
Thornton took to Twitter on Wednesday afternoon.
Thxs to the Sacramento organization and most of all the fans for showing me love since my 1st day in sac really appreciate it- Marcus Thornton (@OfficialMT23) February 19, 2014
Hello Brooklyn- Marcus Thornton (@OfficialMT23) February 19, 2014
Sources told ESPN.com that the Nets' first choice was to trade for Cleveland's Jarrett Jack. But the Cavaliers' reluctance to take Terry scuttled those talks. The Nets then turned their attention to Thornton, who is having a down season with Sacramento. The Nets hope he can provide some added offensive punch off the bench.
The Akron Beacon Journal reported earlier Wednesday that the Thornton trade was nearing completion.
Thornton is averaging 8.3 points per game and 38.1 percent shooting this season. In 2010-11, he averaged 21.3 points and followed that up by averaging 18.7 points in 2011-12.
In his first season with the Nets since coming over in the Paul Pierce and Kevin Garnett trade during the summer, Terry has averaged 4.5 points in 35 games. The 6-foot-8 Evans, known for his rebounding, has appeared in 30 games and is averaging 2.7 points and 5.0 rebounds. He averaged 11.1 rebounds in 80 games last season.
The Nets, sources said, are prepared to complete the deal, despite the fact that adding Hill in this manner will add more than $15 million to this season's payroll and take it beyond the $200 million mark. Sources say the Lakers haven't yet committed to deal him to Brooklyn, and both Phoenix and Dallas have inquired about Hill, according to a league source.
Hill, who has found it difficult to receive consistent playing time in Lakers coach Mike D'Antoni's rotation, said he wants to stay in L.A. but wants a bigger role.
"I'm having a ball here, but when I'm here, I do want to play," Hill said. "I love my teammates, I love the coaching staff, I love everybody [with] the Lakers. I've had a great time here, if anything does happen."
Information from ESPNLosAngeles.com's Dave McMenamin contributed to this report.