Treadwell has been Michigan State's offensive coordinator and receivers coach the past four years. He was chosen Friday to take over for Haywood, who left for Pittsburgh after two seasons in Oxford.
Treadwell was a team captain and four-year starter at Miami from 1978 to 1981. He becomes the school's 34th coach. In a statement Friday, Miami (Ohio) said Treadwell will be "re-introduced" in a news conference Jan. 10 at the university.
"It's a dream come true to return to my alma mater, Miami, as head football coach," Treadwell said in a statement released by the school. "Miami has always held a special place in my heart, and the opportunity to be a part of the 'Cradle of Coaches' is a privilege as well as a responsibility."
Treadwell filled in for Michigan State's Mark Dantonio as acting head coach for two games after Dantonio suffered a mild heart attack earlier this season.
Miami (9-4) plays in the GoDaddy.com Bowl on Jan. 6 against Middle Tennessee State. Miami said Treadwell will attend the game.
Michigan State (No. 9 BCS, No. 7 AP) plays Alabama (No. 16 BCS, No. 15 AP) Saturday in the Capital One Bowl.
Information from The Associated Press was used in this report.