Ranaudo, 25, made his major league debut with the Red Sox last season, going 4-3 with a 4.81 ERA in seven starts.
Considered one of several high-ceiling pitching prospects in the Boston organization, Ranaudo was named the International League's most valuable pitcher in 2014, leading the IL in wins (14) and ERA (2.61).
Ross, 25, started 12 games for the Rangers last season, struggling as a member of the rotation (1-6, 5.70 ERA) before being switched to the bullpen, where he enjoyed success in 2012 and '13 (2.62 ERA in 123 games combined). He went 3-6 with a 6.20 ERA overall in 27 games in 2014.
The 6-foot-7 Ranaudo is headed to the team he failed to sign with after being drafted out of a New Jersey high school in the 11th round of the 2007 draft.
Ranaudo then went to LSU and was taken by Boston as a supplemental first-round pick in the 2010 draft.
"He is a guy we like, we've liked for a long time," Texas general manager Jon Daniels told The Associated Press in a call from the Dominican Republic. "When this trade came down, we liked the value."
Ranaudo, described by Daniels as having a quality four-pitch mix and a strike-thrower, will go to spring training in competition to be the No. 5 starter for Texas. If not in the Rangers' rotation, Ranaudo most likely will go to Triple-A Round Rock.
Ross was optioned to Triple-A Round Rock in June, where he eventually returned to the rotation and posted a 4.33 ERA in 12 games (nine starts).
Given the Red Sox's crowded starting rotation and need for lefty out of the bullpen, Ross likely will be moved back into a relief role.
Information from The Associated Press was used in this report.