Porter, 25, is averaging 12.6 points, 5.6 rebounds and 2.0 assists per game this season. He is making $26 million this season and is owed $27.25 million next season, with a player option for 2020-21.
Portis will become a restricted free agent this summer.
The Bulls have been trying to trade Parker, who has a team option for next season worth $20 million.
Portis and Parker left Chicago's United Center shortly before the Bulls tipped off against the New Orleans Pelicans on Wednesday. Parker was expected to leave for Washington on Thursday morning, his father told ESPN.
Several Bulls players said they were sad to see Portis and Parker go. Bulls guard Zach LaVine called Parker "the main glue of the team, a big-time voice."
"It sucks. He's one of my best friends on the team," LaVine said. "Jabari and me talk all the time. It sucks he didn't get the way he wanted to come here. A Chicago kid, I don't think he got the fair end of the stick on that one. It's the NBA, man."
"Those two are great players, and they're gonna go out there, and they're going to be ready. Y'all know how I feel when I play against Minnesota," added LaVine, who began his career with the Timberwolves. "They're going to feel the same way playing against us."
News of the trade reached the Wizards' locker room about a half-hour before the team's game against the Milwaukee Bucks.
"It was a little weird," Wizards guardBradley Beal said. "But you have to be a professional about everything. Decisions are made. People come and go. It's unfortunate. Otto was a part of the franchise for a long time. All we can do is continue to move on."
The trade comes one day after the Wizards announced that star point guard John Wall, already out for the season with a left heel injury, will miss most -- if not all -- of next season because he needs surgery on his left Achilles tendon.
"It has been a heckuva week, I can tell you that," centerThomas Bryant said. "Dealing with injuries, guys getting traded. We just have to stick together. No one is going to feel sorry for us. We got to get out and fight through this each and every game."
Washington's two trades will provide significant financial savings, moving the team $232,000 below the luxury tax threshold. Since the start of the season, the Wizards have saved $18.3 million toward the luxury tax.
Parker's $20 million team option needs to be exercised by June 29. Portis is on an expiring contract, and the Wizards will have until the end of June to submit a $3.6 million qualifying offer.
Beal said he is confident Porter will acclimate to his new team quickly.
"I know what he is capable of doing," Beal said. "He has the ability to go lead a young team now. I know he will do well there. We will welcome Bobby, and we got Jabari too, right? So we will welcome both of them and keep moving forward."
ESPN's Bobby Marks, Michael C. Wright and Malika Andrews contributed to this report.