According to Fox Sports, the Rangers will get rookie reliever Corey Knebel and minor league pitching prospect Jake Thompson. The Fox Sports reports, both via Twitter, also said the deal was pending physicals.
Soria has 17 saves, 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 on Tuesday night against the New York Yankees.
The Rangers lost the game 2-1 in 14 innings.
Last week, Rangers general manager Jon 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 on Tuesday, Soria had converted his last nine save opportunities.
Knebel, 23, was selected by Detroit with the 39th overall pick in the 2013 draft out of the University of Texas. He has a 6.23 ERA and 11 strikeouts in 8 2/3 innings with the Tigers this season.
Thompson, 20, was a second-round pick in the 2012 draft. He went 6-4 with a 3.14 ERA for Lakeland in the Class A Florida State League before a recent promotion to Double-A Erie.
Baseball America ranked Thompson as Detroit's No. 4 prospect and Knebel as the Tigers' No. 6 prospect before this season.
Information from ESPN.com's Jerry Crasnick was used in this report.