Fultz will meet with the Celtics and also undergo medical testing on Monday, and then will work out for the team on Tuesday morning, a source told ESPN.
Fultz told ESPN last week that he is hopeful of being selected by the Celtics with the top pick in the NBA draft on June 22.
"I want to be the No. 1 pick really bad," Fultz said. "It's been a dream of mine since I was a little kid, and I feel like I would fit well in Boston."
Fultz, who has never visited Boston before, is expected to meet with president of basketball operations Danny Ainge and the rest of the Celtics brass.
Fultz met with Ainge and other Celtics executives in Chicago last month prior to the draft combine. Fultz said he has spoken to Ainge several times since the meeting.
In his freshman campaign at Washington, Fultz averaged 23.2 points, 5.9 assists and 5.7 rebounds.