Rangers general manager Jon Daniels said Nippert will be part of the roster on Opening Day.
"He's going to take that last bullpen spot," Daniels said. "He's a big, durable guy who we feel can do many different things for us."
With the move, Daniels said pitcher Wes Littleton will be optioned to Triple-A Oklahoma, while right-hander Robinson Tejeda will be designated for assignment.
"That was the toughest part," Rangers manager Ron Washington said. "Both Robinson and Wes came so close. It's tough to tell them this close to the real deal."
Washington said Nippert provides some valuable postseason experience, having pitched for Arizona against the Colorado Rockies in last season's National League Championship Series.
Nippert made 36 relief appearances last year for the Diamondbacks, going 1-1 with a 5.56 ERA in 45 innings. The 6-foot-7 right-hander held left-handed batters to a .238 average last season.
Nippert has struggled so far this spring. But even with an 14.40 ERA, Washington said he's not worried and is excited to have Nippert on board.
"You can't take too much into spring numbers," Washington said. "There are times when people have great springs and have horrible seasons, while there are other times when you have rough springs but great seasons."
Marte split time last season between Class A Bakersfield and Clinton, leading Bakersfield with 11 saves.
"Dustin's been a starter in the past, but he's also been an effective late-inning reliever," Daniels said.
Had Nippert's wife not delivered on Friday, Daniels said he would have hoped Nippert could pitch one inning on Saturday. Daniels said he hopes Nippert will be in uniform on Opening Day against Seattle.
Nippert was drafted in the 15th round of the 2002 First-Year Player Draft out of the University of West Virginia.
Washington also announced that Milton Bradley will not begin the season in the outfield. Bradley will be the designated hitter for Opening Day against the Seattle Mariners.
Washington said Bradley is rounding into form at the right time. Bradley notched his first homer of the spring on Thursday and added a two-run single in Friday night's defeat against the White Sox.