Wade agreed to leave about $8 million of his $23.8 million salary on the table after talks between the two sides about a resolution intensified ahead of Monday's start of training camp.
Wade has a long-standing relationship with LeBron James, who attempted to recruit Wade to Cleveland last summer, but the Cavs didn't have salary-cap space at the time. James and Wade have kept in touch this summer about Wade's options, sources said.
In addition to the Cavs, the San Antonio Spurs, Miami Heat and Oklahoma City Thunder are contenders for Wade once his buyout becomes official, sources said. Wade also has a close relationship with Carmelo Anthony, who will officially become a member of the Thunder on Monday.
Wade, speaking to The Associated Press on Sunday night, indicated that he might decide his next move quickly.
"I'm going to take tonight and some of tomorrow and speak to the teams or players that are on my list and go from there," Wade said. "My decision is a pure basketball decision, and I'll make the one that fits me best at this point in my career and with what I feel I have to offer a team that needs what I have to offer."
Wade, 35, said it was fulfilling a lifelong dream to play for the Bulls.
"As the people around me knew, if I ever left Miami, playing in my hometown was something I needed to do before my career ended," Wade told ESPN's Ramona Shelburne. "So I am thankful to the Bulls for that opportunity to live out a dream I've always had as a kid.
"Now I'm excited about what's next. I wanna get back to high expectations and competing at the highest level there is in our sport."
He also tweeted his thanks to Chicago and its fans.
A Dream was fulfilled!!! Thank you Chicago!!!
— DWade (@DwyaneWade) September 25, 2017
Last week, Heat president Pat Riley hinted at the team's desire to bring Wade back: "Anything that happens from a personnel standpoint down the road or any opportunities that are there, we're always going to approach that," Riley said about Wade.
Among Wade's expected suitors, the Heat currently would have the most money available to offer, at $4.2 million. The Spurs have $3.3 million, and the Cavs have $2.5 million. The Thunder could offer only the minimum salary, which is $2.3 million. It would be most costly for the Cavs, as they would pay $10.5 million in luxury tax if they added Wade.
"When Dwyane acknowledged that he wanted to play for a contender and didn't want to be part of a rebuild, look, we worked with him, he worked with us and it became something we were able to do this weekend,'' Bulls vice president of basketball operations John Paxson said Monday. "Like we said, we wish him all the best. He'll do great.''
Chicago had reason to still give Wade roughly $15 million of his salary for the season, as they are still below the mandated salary floor. Earlier Sunday, the team agreed to a new contract with free agent Nikola Mirotic.
Wade averaged 18.3 points, 4.5 rebounds and 3.8 assists in 60 games last season.
ESPN front-office insider Bobby Marks contributed to this report.