Turgeon, 42, met with Texas A&M athletic director Bill Byrne this morning and reached an agreement.
The Shockers won the Missouri Valley conference championship and went to the Sweet 16 two years ago. Wichita State was arguably the hottest team in the country early this past season, but Turgeon's team suffered key injuries and didn't make the postseason.
Wichita State was 17-14 this past season and 111-76 in Turgeon's seven-year tenure. Turgeon has recruited well in the Lone Star state, so it would be a spot where he could further take advantage of his relationships in Texas.
Turgeon makes $750,000 per season at Wichita State, but Texas A&M could pay him nearly double. Gillispie was slated to make in excess of $1.5 million per season before he bolted for Kentucky last week.
Turgeon will take over a program that was 27-7 last season, advanced to the Sweet 16 and is building a new practice facility. However, the Aggies will lose standout guard Acie Law IV and forward Antanas Kavaliauskas.
A key for Turgeon is whether he'll be able to keep 6-foot-11 DeAndre Jordan, one of the most talented big man in the senior class. Jordan could team with Joseph Jones to form one of the most potent 1-2 frontcourt duos in the country. The Aggies also have guards Josh Carter and Dominique Kirk coming back.