Burton averaged 10.3 points and 3.4 assists per game as a sophomore at Wichita State, where the 6-foot-4 guard played 67 games overall the past two seasons.
If the NCAA adopts a proposed change to allow Division I athletes to transfer once without sitting out a season, Burton could become eligible to play next season for the Red Raiders.
Texas Tech coach Chris Beard announced Burton's signing on Thursday.
Burton is from Charlotte, North Carolina. He helped lead Independence High School to the North Carolina Class 4A state championship as a senior.
Sophomore forward Joel Ntambwe had to sit out last season for Texas Tech after transferring from UNLV. The NCAA denied an eligibility waiver for Ntambwe.