Right-handed pitcher Jake Lemoine, Texas' fourth round pick, signed for $528,000.
The Rangers' other signees are shortstop Dylan Moore (seventh round), right-handed pitcher Blake Bass (eighth round), right-handed pitcher Peter Fairbanks (ninth round), shortstop Leon Byrd (10th round) and center fielder LeDarious Clark (12th round.)
"I'm very excited and blessed and fortunate to have this go so smoothly," Tate said of signing with the Rangers. "I'm ready to get going. I have a lot of work to do, and I'm excited to get to work."
Tate was a 2015 Louisville Slugger All-American and Golden Spikes Award semifinalist this past season as a junior at UC Santa Barbara. He went 8-5 with a 2.26 ERA in his first college season as a starting pitcher.
"We look at that as a positive," general manager Jon Daniels said. "You've got a guy with a fresh arm, an electric arm and a guy willing to put in the work and ask the right questions to improve. No doubt, a definite starter for us."
Tate -- a product of Major League Baseball's Urban Youth Academy in Compton, California -- was soft-spoken but also articulate at his press conference. Daniels said Tate's intelligent demeanor has always impressed the team in past meetings.
Tate has an upper-90s fastball and a plus breaking ball and named David Price as a pitcher he tries to pattern himself after. But Tate has recently tried to transform himself into more than a power arm.
"I think I've always been kind of obsessed with pitching and the craft of the whole thing and keeping hitters off-balance," he said. "That has evolved over time. I started to slowly and slowly get more into it and kind of recognize the game within the game."
Tate and five of the other draftees have been assigned to the Spokane Indians of the Northwest League. The lone exception is Lemoine, who will initially go to the Arizona Summer League before heading to Spokane.
Lemoine, a University of Houston product who grew up a Rangers fan, is still recovering from March shoulder surgery.
Rangers scouting director Kip Fagg said the plan is for Tate to get four or five starts this summer on a development path similar to that of Chi Chi Gonzalez. Daniels said the organization would like to see about 20 innings from Tate this summer.
"He's not going to pitch every fifth day," Daniels said. "It's going to be a little bit of a different setting. The long toss program, the throwing program, all the other stuff that goes into it.
"It's more of getting him indoctrinated to the program so he goes into '16 without any limitations."