The Cubs acquired right-handed pitcher Barret Loux and a player to be named from the Rangers on Tuesday for Brigham, a right-handed pitcher, who was acquired in July from Texas for catcher Geovany Soto.
Brigham had been on the Cubs' 40-man roster. Loux does not need to be added to the 40-man.
Loux, 23, was named the 2012 Double-A Texas League Pitcher of the Year after going 14-1 with a 3.47 ERA in 25 regular-season starts with Frisco. He helped the team reach the Texas League Championship Series, led the league in wins and finished sixth in ERA while striking out 100 batters and walking 41 over 127 innings.
Originally selected by the D-backs sixth overall in the 2010 Draft out of Texas A&M, Loux was declared a free agent by Major League Baseball and signed with the Rangers on Nov. 18, 2010. He was a finalist for the Golden Spikes Award, presented annually to the nation's top amateur player.
Brigham, 24, was assigned to Double-A Tennessee after being acquired by the Cubs, but he was limited to two starts, going 0-2 with a 19.64 ERA because of right elbow strain that ended his season. When they made the trade in July, the Cubs and Rangers had agreed to revisit the deal at the end of the season.
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.