Johnson, who is ranked the club's No. 11 prospect by MLBPipeline.com, was headed to Boston on Thursday and was set to undergo an examination on Friday, said manager John Farrell.
Right-hander Hector Velazquez will take Johnson's spot in the rotation and start Monday at Kansas City. Velazquez, who was called up Wednesday, took over for Johnson and threw 3 1/3 innings of scoreless relief for his first Major League win.
Meanwhile, Maddox will add another arm for the Red Sox's bullpen. Maddox has so far posted an excellent season between Double-A Portland and Pawtucket. In 27 innings, the 26-year-old has registered a 1.33 ERA and a 1.037 WHIP in 18 games.
"I've been staying true to myself. Staying within myself, and trusting myself and attacking hitters," Maddox said of his 2017 season.
The move might be bittersweet for the two pitchers, as they were teammates at the University of Florida before being selected in the 2012 Draft by the Red Sox. Johnson was taken in the first round, while Maddox heard his name called in the third round.
To make room for Maddox on the 40-man roster, Boston transferred left-hander Roenis Elias to the 60-day DL.
Stephen Pianovich is a contributor to MLB.com based in Philadelphia and covered the Red Sox on Thursday. This story was not subject to the approval of Major League Baseball or its clubs.