Philip Dunne, MP for Ludlow, is the last of the county's Conservative MPs to reveal their choice for the next leader of the party.
The former health minister had held a public survey to gauge opinion on the contest.
Confirming his decision Mr Dunne said he believed Mr Sunak was more likely than Liz Truss to have the broad appeal required to win a general election – highlighting the succession of recent defeats in by-elections as evidence for the need to widen the party's appeal.
He said: "The by-election losses of rural seats in North Shropshire and Tiverton & Honiton over the last eight months is a stark reminder that we as a party must appeal to a broad cross-section of voters, not just our traditional Conservative base.
“This is a difficult decision, as is clear from my survey, as we have two strong and experienced Conservative candidates to choose between.
"After considerable thought I am persuaded that Rishi Sunak is best placed to provide the strong leadership we need to cope with the significant challenges we face.
"He is also more likely to appeal to swing voters beyond our core vote and is thus the best candidate to win the next election.
“Whoever is chosen as leader on September 5, I have every confidence that our country will be in safe hands. But I shall be voting for Rishi in the membership ballot."
Mr Dunne said that he was not convinced that the polling showing Liz Truss as favourite was as accurate as portrayed – with it being difficult to poll exclusively Tory party members, who are the only ones eligible to vote in the contest.
He said: "The opinion polling that has been done is – by admission of the pollsters, almost impossible for them to poll Conservative Party members. They are few and far between.
"I have seen that they would have to ring something like 100,000 people to get a sample of members and even that would be very difficult to balance.
"I think as a result you have bad opinion polls and the bookies have it wrong and it is much closer."
Mr Dunne said that his own survey, which had 1,259 responses, had shown 36 per cent support for Sunak and 32 per cent support for Truss – with the rest either undecided or not making a response.
He said that when broken down into party members the results showed 35 per cent support for Truss, and 33 per cent for Sunak, with 32 undecided.
He added: "I think this is wide open and the undecided members will make the decision."