Thornton, 21, was used primarily in the bullpen this year, striking out 81 batters in 62 innings pitched with six saves for the Tar Heels. He was converted to a starter as a sophomore and was named second team All-ACC after being named freshman All-American in 2013.
"It's been a childhood dream to be drafted," said Thornton, who said he plans to fly to Florida soon for his physical before reporting to Tri-City. "The Astros have made it a reality."
After being taken by the Astros, Thornton heard from Astros Minor Leaguers Kent Emanuel, Brian Holberton and Colin Moran, all of whom also played at North Carolina.
"[Emanuel] actually texted me on the day I got drafted and said, 'Welcome to the organization. You're going to love it. They treat you well and you have a lot to look forward to.'"
Stubbs, 22, set career highs in almost every offensive category in his senior season, batting .346 with 15 doubles, 25 RBIs, 27 walks and an .869 OPS. He was named a finalist for the Johnny Bench Award, given to the nation's top college catcher. He threw out 52.8 percent of would-be basestealers.
"It's been an unbelievable experience going through the Draft and seeing my name pop up on the board," he said. "The Astros are an organization that's building and that's fun to be a part of. The team, from what I understand, they're doing well and they have a lot of great players.
"It's an exciting organization to be a part of, and I think I can speak for me and the other guys that got drafted. It's an organization that's bringing players up and I want to be one of the players to move through the system as fast as possible."
Stubbs will also report to Tri-City.
Brian McTaggart is a reporter for MLB.com and writes an MLBlog, Tag's Lines. Follow @brianmctaggart on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.