Barnett, who has been working at ESPN since 1996, was born and raised in Denton and graduated from the University of North Texas.
He still lives in Denton with his wife, Kim, and their two children.
"The Rangers are thrilled to be adding Dave Barnett to our radio broadcasts," Rangers president Nolan Ryan said. "Dave is an accomplished announcer with strong Texas ties who will bring passion and knowledge to our broadcasts. He and Eric Nadel will make a great radio team."
Barnett was voice of the Dallas Mavericks from 1981-88.
From 1988-96, he was the lead television broadcaster for the San Antonio Spurs but also spent 1990 doing the Rangers' cable telecasts.
He also did Southwest Conference football and basketball for Raycom Sports.
Barnett moved to ESPN in 1996 and currently calls Big Ten football and basketball and Major League Baseball on both television and radio.
He will continue to work for ESPN on football and basketball in the offseason and will do some Rangers television when Josh Lewin is away on other assignments.
"I had no idea this was going to come open," Barnett said. "But I have been looking over the past few years to see if there was a situation like this that could go along with what I do at ESPN. This is ideal. I'll still do basketball and football for ESPN, but I was looking for a situation where I could be a part of a team family and a team broadcast every night. Those situations are few and far between."
Barnett replaces Victor Rojas, who took a job with MLB Network last month, and will be the No. 2 broadcaster on the Rangers radio behind Nadel, who going into his 31st season with the franchise.
"I'm really looking forward to that," Barnett said. "I've known Eric for almost the entire time he has been with the Rangers. I have been a huge fan of Eric's almost from Day 1."
Nadel, who has been the lead broadcaster on radio since 1995, had significant input into the hire.
"When I learned that Dave was interested in the position, I was extremely excited," said Nadel. "As the process unfolded and I realized this was going to work out, I was ecstatic."