The leadership contest winner will replace former prime minister Rishi Sunak, who stood down as party leader after leading the Conservatives to their worst performance at a general election in July.
Former home secretary Priti Patel went out in the first round of voting by Tory MPs in September, followed by shadow pensions secretary Mel Stride a week later.
The days before the results were announced saw a flurry of endorsements for the leadership candidates.
Cleverly received a boost on Monday when he was backed by former leadership candidate Stride, who won 16 votes in the last round. In total, Cleverly gained 18 votes compared to the last round.
Hamble Valley MP Paul Holmes quit as a Tory whip in order to also publicly support Cleverly on Tuesday.
While Badenoch received endorsements from former cabinet minister David Davis and another from the Governor of Florida Ron DeSantis.
The BBC understands ex-prime minister Rishi Sunak did not vote in the leadership election and does not plan to endorse a candidate.
