The deal is pending physicals and sends rookie right-hander Corey Knebel and right-handed minor league prospect Jake Thompson to Texas.
Knebel will be assigned to Triple-A Round Rock, with Thompson going to Double-A Frisco.
"Corey Knebel is a big physical right-handed guy with back of the bullpen speed and demeanor," Rangers general manager Jon Daniels said. "A power fastball, curveball combo, a lot of success at [the University of Texas]."
Knebel, 22, made eight relief appearances for the Tigers this season, allowing six earned runs in 8 2/3 innings.
He was recalled from Triple-A Toledo for a second stint with the Tigers on July 19. His first appearance in the big leagues came against the Rangers on May 24 in Detroit.
Daniels said the fact that Thompson, from Rockwall, Texas, was being assigned to Double-A at his age was a positive, given the amount of talent at that classification.
Thompson, 20, had gone 7-4 with a 3.06 ERA in 18 starts for Lakeland (high Class A) and Erie (Double-A) this season.
"Big, physical kind of guy, built for innings, a four-pitch mix," Daniels said of Thompson. "Good life on the fastball and a good slider. A good makeup."
Soria had 17 saves and a 1-3 mark with a 2.70 ERA in his second season with Texas after five years as Kansas City's closer.
In his last appearance for the Rangers, Soria blew a 1-0 lead in the 13th inning for his second blown save of the season Tuesday night against the New York Yankees.
The Rangers lost the game 2-1 in 14 innings.
Last week, Daniels said he was open to trading several players who were entering the final year of their contracts. The Rangers had a club option on Soria at $15.7 million with a $500,000 buyout.
Before blowing the game Tuesday, Soria had converted his previous nine save opportunities.
"I'm going to a new team, and that's going to be my new family and I will do whatever they want me to do," Soria said of the Tigers, where he likely will become a setup man to Joe Nathan. "I want to help them win the World Series -- that's what this is all about -- and I hope to help them out as much as I can."