Mr Hunt, the Foreign Secretary, has made up some ground on Boris Johnson amid the former Mayor's relative lack of public appearances and refusal to answer questions about a domestic disturbance at the London flat he shares with his girlfriend.
Ms Davidson previously backed Sajid Javid for the leadership, lauding his vision to 'unite Britain'.
However, the Home Secretary was knocked out at the penultimate round of MPs voting, leading Ruth Davidson to switch her preference to Environment Secretary Michael Gove, who lost out by two votes in the final round to determine which two candidates would face the Conservative Party membership.
Scottish Conservative leader Ms Davidson tweeted earlier this afternoon: "Any Conservative leadership candidate must put the Union first. Jeremy has done so and will get my vote."
She linked to a newspaper article quoting Jeremy Hunt as saying that the preservation of the Union would take precedent over all other policy matters, including Brexit.
Ms Davidson has previously apologised to giving the 'kiss of death' to Mr Javid and Mr Gove.
The Edinburgh Central MSP previously clashed with Boris Johnson during the Brexit referendum, and even banned him from this year's Scottish Conservative Party conference in Aberdeen.
Her tone has softened in recent weeks, however, claiming that she would campaign for Mr Johnson in a General Election.
Mr Hunt has made the union a cornerstone of his campaign, saying he is a Unionist to his core and using a weekend visit to Scotland to tout his credentials as the candidate that Nicola Sturgeon fears most.
Despite his recent troubles, Boris Johnson remains the frontrunner and odds-on favourite to be announced as the successor to Theresa May in July.