Turner had been dismissed from the program last week, but met with Strong on Wednesday and agreed to conditions to remain a member of the team, the source confirmed.
Turner played in 12 games last season, making three starts and recording 37 total tackles. He is projected to be the starter at free safety this season.
Three other players dismissed last week -- running backs Joe Bergeron and Jalen Overstreet and defensive back Chevoski Collins -- are not expected to return to the program. Bergeron, a senior, is reportedly interested in playing this season at the Division II level.
Texas has yet to confirm any dismissals and the three departing players remain listed on Texas' official roster.