The Celtics had targeted Walker, 29, as the No. 1 priority in free agency and an elite replacement for the departing Kyrie Irving.
Walker met with the Celtics on Sunday when free agents were allowed to begin negotiating agreements with teams. Contracts can be officially signed July 6.
Walker is coming off the best season of his eight seasons with the Charlotte Hornets, averaging 25.6 points while playing in all 82 regular-season games.
Walker called the decision to leave Charlotte "one of the toughest things that I definitely have had to do in my career."
"The hardest part for me is having to leave the city and organization that I've been a part of for eight years," he told ESPN's Scott Van Pelt. "The organization that gave me my first opportunity to go from a boy to a man in this league. Charlotte, the place that I love very much. It was a really tough decision. But you know, it was something I had to do in order to try and fulfill some dreams of mine and compete."
Kemba Walker tells SVP that the idea of the Celtics meant winning when he was growing up, and playing for Boston gives him to best chance to do so.
After a season of locker room turmoil often centered around Irving's discontent, the Celtics crave the stability and leadership that Walker will provide -- in addition to being an All-Star talent in the prime of his career.
Walker can plug into a Celtics lineup that includes Jayson Tatum, Gordon Hayward and Jaylen Brown. Boston can still pursue a center with its $4.8 million exception and build a team that could be competitive in the Eastern Conference.
"When you think of the Celtics, you think of championships," Walker told Van Pelt. "You think of winning, and that's what I am about. I'm about competing for championships and winning. That's something I haven't been able to do throughout the early years of my career. I haven't been a consistent winner in this league. I just felt like Boston was the best fit for me to try and accomplish those kind of goals."
Charlotte, meanwhile, brings in Rozier as Walker's replacement. Rozier, selected 16th overall in the 2015 draft, had his best season in 2017-18, when he averaged 11.3 points a game filling in for an injured Irving.
The Hornets also declined to exercise their qualifying offer on Frank Kaminsky, allowing him to become an unrestricted free agent amid significant interest, a league source told ESPN.
Walker won a national championship at UConn in 2011 and is a New York City native.