Johnson is coming off a season in which he averaged 9.2 points and 6.1 rebounds in 71 games for the Toronto Raptors. The forward spent the last six seasons in a Raptors uniform after four years with the Detroit Pistons.
Johnson was the last player signed out of high school before the NBA changed its rules to require players be at least one year removed from their senior year of high school before they can enter the NBA draft.
As it stands now, Johnson will be the highest paid player on the Celtics roster ahead of Gerald Wallace's $10.1 million salary.
Johnson can not officially sign his new contract until July 9, when the NBA lifts a moratorium on player business.