Brown, 22, is part of the NBA’s draft class of 2016 that is eligible to sign rookie extension deals prior to a 6 p.m. ET Monday deadline.
Glushon and Celtics general manager Danny Ainge negotiated most of the deal’s details over the weekend in Boston.
This is the first rookie-scale contract extension that Ainge has done since Rajon Rondo in 2009.
Brown, the No. 3 overall pick out of California, has steadily developed into one of the league’s top young forwards. He’s averaged 11.2 points in three NBA seasons, including 13.9 in last year’s playoffs and 18 points a game in 18 playoff games in the 2017-18 postseason.
Brown was a starter for Team USA in the FIBA World Cup over the summer.