"Kelly has done an outstanding job representing our Nation and I have no doubt that, under her leadership, our Country will be represented at the highest level," Trump tweeted.
Kelly, 56, had been rumoured as a possible choice for the position. If approved by the Senate, Kelly will succeed Nikki Haley, who stepped down at the end of 2018.
Craft, originally from the state of Kentucky, founded a marketing and business advisory firm, and in 2007 was appointed by president George W Bush as an alternate delegate to the UN General Assembly, according to her biography at the State Department website.
Her husband, Joe Craft, is a billionaire coal-mining executive. They are both Republican donors, and according to the Washington Post, gave around 1.5 million dollars to support party candidates in the 2016 election.
The Post also reported Friday the Crafts have been "repeat high-paying customers" at Trump's hotel in Washington.
Craft has also served in leadership roles with the Salvation Army of Lexington, Kentucky and the Center for Rural Development, a non-profit dedicated to economic development in rural Kentucky.
In a 2017 interview with broadcaster Canadian broadcaster CBC, Craft said in response to the question whether she believed in climate change: "I believe there are scientists on both sides that are accurate."
State Department spokeswoman Heather Nauert, Trump's first choice to succeed Haley, earlier this month withdrew herself from consideration, saying it was in the best interest of her family.
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