The Astros introduced Eshelman, the No. 46 overall pick out of Cal State Fullerton, on Wednesday. MLB.com's Jim Callis reported the deal is for $1.1 million, though the club has not confirmed the value.
The addition of Eshelman means the Astros have signed every pick in the first 10 rounds and 33 of their 42 overall picks in this year's Draft.
Director of scouting Mike Elias said Eshelman will be sent to the Gulf Coast League, but he will be kept to a strict schedule due to the 137 innings Eshelman threw this season in college.
• Draft Bonus Tracker
"We don't have a desire for him to go out and log a ton of innings this summer," Elias said. "We want to keep his innings totals in line with what he did last year and what we expect out of him next year. He'll ramp up slowly an after some rest and get back into game shape and I expect he pitch a little [in the Gulf Coast League], then possibly see an assignment after that. Ultimately, I don't see him throwing a ton of innings this year, we'll work toward gearing him up for Spring Training next year."
Eshelman was named the Big West Conference Pitcher of the Year and finished the season with a 1.58 ERA. He logged 139 strikeouts in 137 innings, issuing only seven walks all season.
"I'm just the kind of guy who goes out there and throws strikes," Eshelman, who had 139 strikeouts in 2015, said. "I try to get the hitter out ultimately and get back to the dugout and win ballgames.
"I'm good to go. Just going to ramp it up and hopefully make a run."
"Thomas has been one of the most successful and durable starters in the country over the last three years," Elias said. "He has a good pitcher's frame, a sound delivery and three Major League quality pitches. His control has been impeccable during his college career and he really knows how to pitch with his fastball. These accomplishments and abilities point to a starting pitcher who should be able to advance steadily in our program, and we are delighted to have signed him today."
Eshelman said going undrafted out of high school was far from discouraging -- in fact it allowed him to gain a deeper understanding of the game and develop the tools necessary to vault up draft boards.
Eshelman said he'll need to refine his slider and possibly add a cutter once he begins pitching professionally and added his emulation of Jake Peavy is another facet of his game he'll carry over.
"I maybe don't have as much emotion as he does on the mound, but his competitiveness and his desire to win, I embed that into my game," Eshelman said.