It puts the Cabinet Office minister at odds with fellow Tories Andrew Lewer and Dame Andrea Leadsom in the six-sided contest to replace Boris Johnson as Conservative Party leader.
Northampton South MP Mr Lewer is supporting former equalities minister Kemi Badenoch while Mrs Leadsom has told South Northamptonshire constituents that trade minister Penny Mordaunt is her choice.
Mr Ellis tweeted: “In Cabinet and in Government, I have loyally served three Conservative Prime Ministers over the past decade.
“I know what it takes to make a good PM. And I have no doubt that Rishi will make a great one.”
Mr Ellis' announcement came before the first round of voting on Wednesday (July 13), which Mr Sunak won comfortably.
A second round of voting on Thursday will see the candidate with the fewest votes knocked out.