Boston signed Ball State University infielder Vitek, its top selection in the 2010 First-Year Player Draft, and Middle Tennessee State University outfielder Brentz, along with the eight other players.
Vitek and Brentz will begin playing with the short-season Class A Lowell Spinners.
"Vitek was a guy who was a follow coming into the year, but really focusing on this year, we kind of fell in love with his bat and his athleticism," said Red Sox general manager Theo Epstein.
The 20th overall selection in the Draft, Vitek, who played primarily second base in college but will be groomed as a third baseman in Boston's farm system, was recently named the 2010 Mid-American Conference Player of the Year. The infielder led the league with 73 runs, tied for second with 17 homers and ranked third with 68 RBIs and 161 total bases.
Earning Louisville Slugger First-Team All-American honors, the junior had a .361 batting average, .691 slugging percentage, 20 doubles and three triples in 58 games.
The righty was ranked the top second baseman in this year's Draft, as well as the third-best pure hitter among college players by Baseball America.
Vitek grew up in Bryan, Ohio, and is a semifinalist for the highly-prestigious Golden Spikes Award.
"It's very exciting to join such a successful organization, and I'm excited to see how they run it and excited to get it all started," said Vitek. "I'm not too familiar with them just because they're not from my area and I didn't grow up on the East Coast or anything like that, but I've always watched them. They've been on TV a lot. I know that they're very successful and run a clean organization, so I'm very excited for that."
Brentz, the 36th overall selection in the Draft, hit .348 with 51 runs, eight doubles, 15 homers and 49 RBIs as a junior in 46 games this season. He also posted a .636 slugging percentage and had a .440 on-base percentage.
As a sophomore during the 2009 season, the right-handed hitter led the NCAA with a .465 batting average, 28 home runs, .930 slugging percentage and 214 total bases. According to Baseball America, Brentz ranked as the third-best power hitter in this year's Draft.
"He was arguably a Top 10 pick coming into this year," said Red Sox director of amateur scouting Amiel Sawdaye. "He's a guy that has light tower, plus raw power. We brought him to Fenway before the Draft and he was wearing out Lansdowne Street. He's someone we're really excited about. He's someone we feel, if all falls well for us, can be a corner outfield bat and another middle-of-the-order of the bat."
The Red Sox have now signed a total of 10 selections for this year's Draft.
Quinn Roberts is an associate reporter for MLB.com This story was not subject to the approval of Major League Baseball or its clubs.