Smith, the coach at Louisville the last five years, accepted the job after contract talks Thursday morning, ending an extensive search that began after Bobby Williams was fired on Nov. 3 after a 3-6 start.
Details of the hiring will be revealed at a Thursday evening news conference at 6:30 p.m. Eastern time.
Smith coached his final game for Louisville Wednesday night, a 38-15 loss to Marshall in the GMAC Bowl in Mobile, Al.
Smith's job status apparently was a contributing factor to the loss as players talked afterwards about how they knew their coach was leaving.
"I want to apologize to the guys," Smith said at a tearful postgame news conference. "Some things got out that hurt us. I don't know if that was the case or not."
Louisville Athletic Director Tim Jurich held a news conference at halftime to announce he gave Michigan State permission to talk to Smith.
"No one knew until halftime and then the word pretty much spread," said star Cardinals quarterback Dave Ragone. "I tried to kind of cool it out a little bit and put some water on the fire, but guys had a lot different emotions at that time. It was hard to regroup and play for something."
Smith went 40-21 in five seasons at Louisville, leading the Cardinals to bowl appearances each year. In 2002, he endured an up-and-down season that started with Bowl Championship Series aspirations behind Ragone, a Heisman Trophy hopeful.
Louisville suffered a season-opening loss to Kentucky, and went just 5-3 in Conference USA and 7-6 overall. At one point, Smith referred to this year as a "season from hell."
Smith, 54, signed an eight-year contract with Louisville in 2000.
While several other schools have filled vacancies, Michigan State had been unable to decide on a candidate, and the school was spurned earlier this month by Washington Redskins defensive coordinator Marvin Lewis.
Morris Watts served as the interim coach after Williams was fired.
Smith's new job will not be an easy one.
Michigan State was considered a preseason contender for the Big Ten Conference title, but the Spartans were just 4-8 in league play, and concluded the campaign with a humiliating 61-7 drubbing at Penn State.
Also, the season included the revelation of a substance abuse problem by quarterback Jeff Smoker that led to his suspension, and star receiver Charles Rogers has decided to enter the NFL draft.
Before coming to Louisville, Smith coached at Utah State and Idaho. He has an overall record of 110-60 record in 14 seasons as a head coach.