Right-hander Michael Kopech, the compensation pick Boston got at No. 33 for the loss of Jacoby Ellsbury, will sign for $1,678,000.
First baseman Sam Travis, the right-handed hitter from Indiana University who was taken in the second round, agreed to a $846,000 contract.
The Red Sox formally announced the Kopech and Travis signings Tuesday.
Chavis has defensive versatility, but is best known for his big bat, which belies his less than imposing physique.
"It's funny, because his ballpark sits right up on a main street, a two-way highway kind of," said Red Sox director of amateur scouting Amiel Sawdaye. "I think, at times, Chavis is trying to hit cars going by. He's launching balls over the left-field wall. But the interesting thing about Michael is when you ask him to go the other way and you ask him to go to right field, he can kind of do it with ease."
The Red Sox can't wait to start developing Kopech, the high school product out of Mt. Pleasant, Texas.
"As far as the mechanics, those of you guys that have seen it, he's got an electric arm," said Sawdaye. "We really like the way he commands his fastball. The delivery kind of reminds a little -- it's got a little Jered Weaver in it."
Travis, who was taken 67th overall, was originally drafted by the Reds out of high school in 2011, but he pursued a collegiate career at Indiana instead.
"Travis is an interesting one, because when you go watch him in BP, from a power perspective, he goes into a BP session and can spray the ball around the field, but then his last round, he'll really let it go," Sawdaye said. "He's another guy that's really going to use the Monster well and then also put some balls onto Lansdowne Street."
One attribute that definitely intrigued the Red Sox about Travis is his ability to control the strike zone.
"The hit tool is very advanced," Sawdaye said. "Excellent recognition skills. He's a guy that can ambush a first-pitch fastball. If he sees it, he's going to be an aggressive hitter, but also has really good plate discipline. He's an interesting one, because, obviously, playing in the Big Ten for Indiana, you don't think of the Big Ten as a major baseball conference. But Indiana played a tough schedule, he faced a lot of really good pitching, and he handled it really well."
Travis hit .347 for Indiana this season -- his junior year -- with 12 homers, 58 RBIs and a .415 on-base percentage. He was named the Player of the Year in the Big Ten.