Houston took Jackson with the 20th overall pick in the draft. He missed the Texans' first training camp workout on Friday morning, but coach Gary Kubiak said Jackson would be officially signed and ready for the second practice of the day in the afternoon.
The Texans expect Jackson to start immediately after longtime cornerback Dunta Robinson signed with Atlanta in the offseason.
The 5-11 Tate, who played at Auburn, has signed his contract and worked out with the Texans on Friday morning. Houston took Tate in the second round of the draft.