Johnson said: "Just signed with the Chicago Cubs! Thanks to God, family, teammates, coaches and friends. If it wasn't for you guys I wouldn't be here!"
Theo Epstein, Cubs president of baseball operations, said they have reached agreement with several of their selections, but they are pending physicals.
The Cubs' No. 1 pick, outfielder Albert Almora, is not included in that group who have agreed to terms. Almora does have a commitment to the University of Miami.
"He's a great student and worked hard to get that full ride to a prestigious university," Epstein said. "He does have options. ... I think he loves baseball, too, and we'll sit down and talk about it."
Epstein was happy with what the Cubs did in the Draft because they were able to address a need for more pitching. Johnson was one of their targets, and Epstein said the right-hander might have been taken in the first round if not for a forearm strain. Johnson was healthy going into the Draft.
"There are a number of guys we're really excited about," Epstein said of the selections.