The AP released the results one day after Miller also was announced as the winner of the SEC's player of the year and freshman of the year awards, as voted on by the league's 14 coaches.
Miller was a first-team pick on all but one AP ballot and received 12 out of a possible 14 player of the year votes and 11 as top newcomer for the regular-season SEC champion and No. 4-ranked Crimson Tide.
The 6-foot-9 forward is only the fourth freshman in the past 50 years to lead the SEC in scoring, averaging 19.6 points along with 8.0 rebounds. He is also tops in 3-pointers made, making 92 and hitting at a 40.4% rate.
Texas A&M's Buzz Williams was named coach of the year Tuesday by the AP in voting by 14 reporters who cover the SEC.
Texas A&M guard Wade Taylor IV and Kentucky forward Oscar Tshiebwe, last year's national player of the year, were unanimous AP first-team picks. The other first-team selections are Missouri guard/forward Kobe Brown and Mississippi State forward Tolu Smith.
Miller's name surfaced in court testimony in the capital murder case of now-former teammate Darius Miles and another man in the shooting death of 23-year-old Jamea Harris near campus.
A police officer testified that Miles texted Miller asking him to bring Miles' gun in the early-morning hours of Jan. 15. Fellow freshman starter Jaden Bradley was also at the scene. Neither has missed a start or been accused of any crime. The university has described Miller as a cooperating witness, not a suspect.
A day after that testimony, Miller scored 41 points and hit the game-winning shot in overtime to beat South Carolina amid jeers from Gamecocks fans. Afterward, Alabama coach Nate Oats called Miller "one of the most mentally tough kids I've ever coached."
Buzz Williams received eight votes, Missouri's Dennis Gates five and Alabama's Oats one in the coach of the year balloting.
Information from The Associated Press was used in this report.