Boyd told MLB.com he expected to sign his contract within the next day or so and report to Tri-City in the New York-Penn League.
"I'm really excited about it," Boyd said. "It's definitely a dream come true. I really didn't expect this day to come. It was amazing."
The pick, which was No. 226 overall, has an assigned slot value of $162,800.
Boyd, a 5-foot-9, 180-pounder, was a junior for the Mountaineers this year and led the team with a batting average of .356. He also tallied 24 RBIs and 18 stolen bases. He garnered All-Big 12 Honorable Mention honors during his sophomore season in which he hit .314 and stole 17 bases.
Gause told MLB.com he planned to sign his deal and will be in the rotation at short-season Tri-City.
"I'm excited, man," Gause said. "I plan on being in the rotation sometime in the next week or so. I've been waiting on this opportunity for two or three years now. I got drafted out of high school (25th round by Indians in 2010) and turned it down and went to college. So I've been waiting for this."
Gause, 6-foot-5, 250 pounds, is coming off a season in which he threw 58 innings and had a 2.17 ERA, along with 83 strikeouts and 24 walks. He is from Shallotte, N.C., and previously attended Walters State Community College.
The pick, No. 286 overall, comes with an assigned slot value of $142,100.
Dykxhoorn is a 6-foot-8, 240-pound pitcher out of Central Arizona College, where he posted an ERA of 2.77 in 78 innings. Dykxhoorn struck out 114 while walking 27.
Dykxhoorn, 19, was drafted in the 20th round out of high school by Cincinnati in 2012 and was a member of Team Canada's junior national team. He pitched in 10 games his freshman season at West Virginia, posting a 3.15 ERA and a 2-1 record. He struck out 20 and walked 11 before moving to Central Arizona College.
"I have basically agreed to a signing bonus -- and it's just the education package and stuff, just minor stuff like that [which needs to be ironed out]," Dykxhoorn told MLB.com. "It's definitely exciting and a bit of a relief, too. I knew what I wanted going in, and the Astros were able to meet it. It was a pretty easy decision for me."
The pick, No. 166 overall, comes with an assigned slot value of $277,400.
Because he's a native of Ontario, Canada, Dykxhoorn said he would need to acquire a work visa before he could report to a Minor League club.