The Florida governor met the business secretary on a trip to Britain ahead of a potential run against Donald Trump to be the next Republican candidate.
He singled out Badenoch for her views on Britain’s cultural debates, during an interview with The Sunday Telegraph.
The paper claimed his allies hope that Badenoch could be the next Margaret Thatcher to their new Ronald Reagan.
DeSantis praised the senior Tory, who is also minister for women and equalities, for her outspoken views.
He described “woke ideology” as “a war on the truth”, telling the paper: “When institutions get infected by woke ideology, it really corrupts the institutions.
“We look at woke infiltrating schools as a problem, woke infiltrating bureaucracies as a problem and woke infiltrating corporate America as a problem. We say that Florida is where woke goes to die.”
DeSantis said Badenoch “complimented what we are doing in Florida” and added: “I commend her and her efforts to make sure that this is not corrupting British society.”
In a post on Twitter following the meeting, DeSantis said she is such a “strong, outspoken leader in the United Kingdom”.
“We share the same goal of spurring economic growth for our people and I look forward to continuing our relationship,” he added.
DeSantis has not announced his intention to run for the Republican nomination but is widely expected to do so.
In his interview, he also addressed speculation over his potential run at the White House, telling the paper: “I’m going to go through our legislative session, get the people’s business done. I’m still in the midst of that.
“I’ve got about another week or so of that, and then I have the Budget and everything. I’m not going to make any decision before then.
“But the end of that time is coming, it’s closer now than it was six months ago. So just stay tuned.”