The host of ITV’s Good Morning Britain made the prediction on his Twitter account. Mr Johnson is the strong bookies favourite to become the next Tory leader. The final decision will be made by an estimated 160,000 Conservative Party members.
On Twitter Mr Morgan commented: “I think Jeremy Hunt will be Britain’s next Prime Minister.”
The next Tory leader will be announced on the week beginning July 22.
In the final ballot of Conservative MPs Mr Johnson had 160 supporters, versus 77 for Mr Hunt and 75 for Michael Gove who was eliminated from the contest.
Mr Hunt has fiercely criticised Mr Johnson for not agreeing to take part in a public debate until July 9, after membership ballots have been dispatched.
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Writing in The Daily Telegraph he commented: “He may be the right man, I may be the right man.
“But Conservative Party members can only make that choice if you have a proper debate.
“And you can’t have that debate if one of the candidates is bottling all opportunities to have a public head to head debate before ballot papers are sent out.
“This is supposed to be his finest hour but if you’re going to hide away, that’s not democracy.”
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Both Mr Johnson and Mr Hunt insist they are the right person to ensure the UK leaves the EU on October 31.
However Mr Hunt campaigned for remain ahead of the 2016 EU membership referendum, meaning he may struggle to pick up support from Brexiteers.
In response to Mr Morgan’s comment Erron Gordon, a series director for Good Morning Britain, replied: “Mystic Morgan has spoken!”
He accompanied it with a photoshopped image of the TV presenter merged with a fortune teller.