Washington State, which became a national title contender under Price, will play Oklahoma in the Orange Bowl on Jan. 1. At Alabama, he succeeds Dennis Franchione, who left to become the head coach at Texas A&M.
Price was is 83-77 in 14 years at Washington State. He guided the seventh-ranked Cougars to a 10-2 record and a share of the Pac-10 Conference championship this season.
"I feel we have hired an outstanding person as well as an excellent football coach," said Alabama Athletics Director Hal Moore.
It is not immediately clear if Price will be allowed to coach the Cougars in Pasadena, but the school moved quickly to find a replacement for Price, promoting long-time defensive coordinator Bill Doba.
The Cougars were 10-2 last year and are enjoying their first back-to-back winning seasons in his tenure. His 1997 team, led by quarterback Ryan Leaf, reached the Rose Bowl for the first time since 1931.
Washington State had three straight losing seasons after that Rose Bowl appearance, but has bounced back handsomely over the past two seasons, with Price recruiting successfully. The Cougars no longer take a back seat to other Pac-10 school.
Price, 56, has no ties to Alabama, and takes over a program that is in the midst of an NCAA probation. The Crimson Tide went 10-3 this season, but are banned from a bowl this season and next as part of NCAA penalties that include scholarship reductions.
The threat of more NCAA penalties was believed to be one reason for Franchione's departure.
New Orleans Saints assistant Mike Riley turned down the job, and South Florida Coach Jim Leavitt withdrew his name from consideration.
Price is known for his ability to develop quarterbacks, and at Alabama he would work with heralded Brodie Croyle, who will be a sophomore next season. Gesser, Leaf and Drew Bledsoe all developed under Price.
Doba has been at Washington State since 1989, and was hired less than a month after Price arrived from Weber State. He has been defensive coordinator since 1994.
Doba, 42, has never been a head coach on the college level. Before coming to Washington State, he was an assistant at The Citadel, Purdue and Indiana.