The announcement could well put to rest the simmering speculation that Franken might be keeping the door open to remain in the Senate, if Roy Moore is elected in Tuesday's Alabama Senate race.
Smith not only would be an immediate placeholder for Franken, but also would run in the November 2018 special election to serve out Franken's term.
"Though I never anticipated this moment", Smith told reporters, "I am resolved to do everything I can to move Minnesota forward, and I will be a fierce advocate in the United States Senate for the economic opportunity and fairness".
Smith's only campaign was as Dayton's running mate in 2014.
"Then we'll know whether his planned resignation was warranted", she wrote, adding: "New facts may put Senator Franken in a better light, or a far worse one, and we should be open to both". She lives in Minneapolis with her husband; they have two grown sons.More news: Nigeria escape 2018 World Cup dismissal
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"I will run in that election and I will do my best to earn Minnesotans' support", Smith said at the news conference. "There are so many different ways of contributing to the future of this state".
In his speech, Franken noted the "irony" that he is resigning while President TrumpDonald John TrumpHouse Democrat slams Donald Trump Jr. for "serious case of amnesia" after testimony Skier Lindsey Vonn: I don't want to represent Trump at Olympics Poll: 4 in 10 Republicans think senior Trump advisers had improper dealings with Russia MORE, who has been accused of sexual misconduct, remains in office.
Franken had spent the past few weeks pleading for forgiveness in response to the accusations.
Standing on the Senate floor Thursday, he said he could no longer be an effective senator for Minnesota but insisted that some of the allegations against him were "simply not true. others, I remember very differently".
Mrs. Smith is going to Washington.
"I will take on this role in my own way using my own judgment and experience", she said. Minnesota will conduct another election for the same seat in November 2020 for a full, six-year term.