Ballot papers will be issued to Conservative party members from later this week in the contest between Boris Johnson and Mr Hunt.
Mr Hague, who served as leader of the opposition between 1997 and 2001, said both candidates had "great merits", but added that he believed Mr Hunt would make the better Prime Minister.
Writing in the Daily Telegraph, the former Richmond MP said: "Both candidates are committed to a policy that will be formidably hard to implement.
"But one of them has left himself the space in which to do it, even if only a little - an important consideration in a parliament the Tories do not control.
"Whoever wins will benefit from much improved national finances, although I would advise more caution over raiding them in the campaign."
"In doing so, however much I wish him well if he is elected, he has lost my vote, because 'do and then die' could very easily be the outcome", he wrote.
"Both men have great merits. But asked to weigh who might make the better prime minister, and have the best chance of avoiding calamity over Brexit, I come to a clear conclusion.
"I will mark my ballot for Jeremy Hunt."