Before working for Dayton, Smith served as chief of staff to former Minneapolis Mayor R.T. Rybak and ran his unsuccessful bid for governor in 2010.
In Carlson's lengthy commentary, emailed to a list of undisclosed recipients, he describes himself as "deeply troubled by the resignation of Al Franken and the complete absence of anything resembling due process".
"Though I never anticipated this moment, I am resolved to do everything I can to move Minnesota forward", Smith said.
Franken said last Thursday he would resign "in the coming weeks".
The race for Franken's seat, which will cost the two sides tens of millions of dollars, will make 2018 one of the most pivotal Minnesota elections in years. Amy Klobuchar, giving Minnesota two female US senators for the first time in its history. The state Constitution says that when the lieutenant governor position is vacated, the Senate president takes over.
Smith served as Dayton's trusted chief of staff for three years before ascending to become his No. 2, and was once considered a likely candidate to succeed him.
The Wednesday news conference will end days of speculation about whom Dayton would send to Washington and also whether the person intends to run for the office or be a caretaker until the special election in November 2018.
Minnesota's governor has chosen Lt. Gov. Tina Smith to fill Sen.
Franken has not yet set a date to leave Congress.
Smith's appointment was widely expected soon after Franken, announced last week that he would step down. Both Democrats spoke on condition of anonymity to speak freely about private discussions ahead of an announcement. The Star Tribune of Minneapolis and Minnesota Public Radio report Smith, 59, will also run for the seat in November 2018.
Smith responded to a text message from an AP reporter seeking comment Wednesday by simply thanking the reporter.
"Further, we know that Senate Democrats who asked for Franken's resignation may have been motivated more by the politics of the Alabama Senate race than the seriousness of the allegations", Carlson writes. At least eight women shared stories of him touching them inappropriately without consent during photo-opportunities, on a celebrity tour to military installations overseas or at political events.
The victor of that election will serve out the remainder of Franken's term until 2020, when they will once again be up for re-election.