The Tribe designated for assignment right-handers Preston Guilmet and Frank Herrmann and lefty Colt Hynes, while reassigning outfielder Matt Carson and infielder Ryan Rohlinger to Minor League camp.
Both Bourn and Giambi will be eligible to return on Saturday, although manager Terry Francona said on Friday that Bourn likely will need longer. The speedy center fielder tweaked his hamstring on March 16 and just recently resumed running the bases.
Atchison and Morgan both were signed to Minor League contracts this winter and were able to earn spots on the club.
The Indians will begin the season carrying 13 pitchers and 12 position players, with the roster breakdown as follows:
Pitchers: Cody Allen, Atchison, John Axford, Carlos Carrasco, Corey Kluber, Justin Masterson, Zach McAllister, Josh Outman, Vinnie Pestano, Marc Rzepczynski, Danny Salazar, Bryan Shaw, Blake Wood.
Catchers: Yan Gomes.
Infielders: Mike Aviles, Asdrubal Cabrera, Lonnie Chisenhall, Elliot Johnson, Jason Kipnis, Carlos Santana, Nick Swisher, Giambi (DL).
Outfielders: Michael Brantley, Morgan, David Murphy, Ryan Raburn, Bourn (DL).
Andrew Simon is a reporter for MLB.com. Follow him on Twitter @AndrewSimonMLB. This story was not subject to the approval of Major League Baseball or its clubs.