A four-star recruit according to Scout.com, Dastrup was listed as one of the top 100 prospects in the country by several recruiting services.
Also signing with BYU were American Fork's Ryan Andrus, Lone Peak's T.J. Haws, Orem's Dalton Nixon and Jake Toolson, a 6-5 wing from Highland High in Gilbert, Ariz.
Haws, Nixon, Dastrup and Toolson are all expected to go on two-year LDS Church missions before enrolling at BYU. Andrus, a 6-10 post player who averaged 19.4 points and 6.5 rebounds a game last year for A.F., plans to play for the Cougars next season.
Also Wednesday, Rose announced that two players currently on missions, wing Jordan Chatman and post player Isaac Neilson, have signed agreements to play for BYU in 2014-15.
"We are very excited about this group of signees," Rose said. "The commitments from these players mean a great deal to our staff and to our basketball program. This group is comprised of great players that will be terrific teammates."
While Dastrup's signing was a last-minute surprise, the other four committed to BYU long ago. Haws is the brother of current Cougar great Tyler Haws, Nixon is the son of former BYU great Kevin Nixon, and Toolson is the nephew of former BYU star Danny Ainge. His father is former BYU star Andy Toolson's cousin.