The highly controversial contract which changes the pay structure for junior doctors in line with his vision of a seven-day NHS led to a series of bitter walk-outs by the British Medical Association (BMA) earlier this year.
While an agreement was reached on in May after more than a year of protracted talks, some junior doctors have said they may still vote against it.
Mr Hunt said if the result of the vote announced on July 6 does not give the contract the green-light he will be “confused”.
Speaking exclusively to the Yorkshire Post, he said: “I think we would all be rather confused because they would be voting against a contract that their own union leader negotiated and supports and said that he was going to encourage them to accept.”
Thousands of operations were cancelled while medics and the Department for Health ironed out how weekend pay would be structured.
Following the agreement made between the Department for Health and junior doctors BMA leader Dr Johann Malawana, members will be asked to vote on whether they agree from June 17 onwards.
Various informal polls have suggested that a majority of members will vote against the contract while those on the left wing of the junior doctors committee have publicly said they will not give it their backing.
Asked if the vote’s result has little bearing on the imposition of the contract, Mr Hunt said he would much prefer a situation where the junior doctors give it their blessing.
Mr Hunt said: “[The vote] is not meaningless because it would be much better to proceed with the changes we need to proceed with, with agreement.
“We do now have agreeent with the leader of the junior doctors committee who spent a long time manning the barricades, and leading his own members out on strike.
“This is someone who is totally familiar with all the details of the new contract. He thinks it’s a good contract so I hope junior doctors will listen to him.”
Mr Hunt said anyone in his position would naturally prefer there to be no strikes from junior doctors, or for it to be their legacy, however rolling out a seven-day NHS is his unfaltering ambition.
The “weekend effect” on the standards of patient treatment is a reality, he said, quoting a study of NHS patients carried out by Professor Nick Freemantle of University College London.
“Alan Milburn is now looked back on as a successful Health Secretary. In his time as Health Secretary there was a huge amount of turmoil but the truth is that he left the NHS with much shorter waiting times than when he arrived.
“I want to leave an NHS with as safetest and best system.
“I hope that is something I can work with doctors because I actually think this is something doctors care passionately about aswell. It hasn’t always been easy through the medium of the BMA to get that message across.”