He led the league in hits (86), on-base percentage (.449) and slugging percentage (.609) at the time of his promotion.
The Cubs signed Kroeger as a minor league free agent this past off-season.
"You always want to make a good first impression," Tennessee manager Pat Listach said of Kroeger. "He's made a lasting impression the way he goes about his business, the way he swings the bat, the way he plays the game."
Kroeger's promotion clears the way for top Cubs outfield prospect Tyler Colvin, who was promoted from Class A Daytona late Tuesday after batting .306 with seven home runs and 50 RBIs in the Florida State League.
Like Kroeger, the 27-year-old Jones also came to the Cubs as a six-year minor league free agent. In 23 games this season, he posted a phantom 0.36 ERA with 33 strikeouts to four walks in 25 innings.
"Geoff has been solid for us and with his delivery, he's been tough on lefties throughout his career," said Cubs Minor League Pitching Coordinator Alan Dunn. "We like what he brings to the bullpen with a different look. He's shown the ability to throw strikes."
Jones also notched six saves in eight opportunities and held opposing hitters to a .151 average against with Tennessee.
To coincide with the move, right-hander Jim Henderson will join the team from Iowa. He was 3-0 with a 5.54 ERA in eight appearances at Triple-A.