Dodgers general manager Ned Colletti made the announcement on Monday.
Elbert earned the honor by going 4-4 with a 3.84 ERA in a combined 20 appearances (18 starts) at Double-A Chattanooga and Triple-A Albuquerque. He struck out 125 batters and walked 44 in 96 innings.
Elbert was selected to play in the Southern League All-Star Game, but he didn't play because he was called up to Triple-A.
Elbert is on his fourth stint with the Dodgers after getting recalled on Aug. 31. He is 2-0 with a 5.29 ERA in 13 appearances this season.
Gordon, 21, also was named the Midwest League Prospect of the Year and league co-MVP with Class A Great Lakes teammate Kyle Russell.
Gordon led the league with 73 steals and 12 triples. He finished second in hits (162) and runs (96).
Gordon was selected as a starter for the Midwest League All-Star Game. He also was on the league's postseason All-Star team.
Elbert and Gordon will be honored in a pregame ceremony during the final home series of the season, when the Dodgers host the Colorado Rockies from Oct. 2-4.
David Ely is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.