Bryant, 22, and Almora, 19, were assigned to the Minor League camp along with Jeudy Valdez, Carlos Pimentel and Eric Jokisch. Their Minor League team assignments will be made at a later date.
Outfielder Aaron Cunningham, 27, who signed as a free agent last November, was granted his release. The Cubs now have 56 players in camp.
Bryant, the second player selected overall last June, hit a home run in his first spring at-bat, and was 2-for-9 in seven Cactus League games. Almora, the Cubs' first-round pick in 2012, had appeared in six games, and was 5-for-9. Soler, coming back from a leg injury last season, was 2-for-8 in eight games.
"We're glad they're Cubbies," manager Rick Renteria said of the top trio. "They've shown their ability to be professionals here in terms of how they carried themselves, some of the performances they had in the course of the spring. Now it's time for them to get down there and start getting more at-bats and start getting ready for the regular season for themselves and continue to develop and improve on their skill sets. It's like anything, all players are a little disappointed, but they know there's a reason and purpose for what we do."
Bryant, Almora and Soler handled themselves well in big league camp, and often had more interview requests than the veteran players on the Cubs roster.
"They showed maturity beyond their age, the way they deal with people, the way they deal with the press, the way they interact with teammates," Renteria said. "It was pretty good."
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.