The university announced the hiring on Sunday. No details of the contract were released.
Curry has spent the last seven years with the Lady Raiders. Her record was 130-98 with Texas Tech, including 21-11 last season and a second NCAA tournament appearance. It was the ninth trip to the tournament for Curry, who was at Purdue for seven seasons before her stint with Texas Tech.
In an Alabama release, Curry thanked the Alabama administration "for the confidence they have shown in me, and for giving me this opportunity. We leave Texas Tech with heavy hearts."