The prime minister was set to face criticism from the opposition Labour party in the House of Commons from 1530 (1430 GMT) although eurosceptics in his centre-right Conservative party broadly support his stance.
Cameron telephoned Juncker yesterday night to congratulate him, and wrote in the Daily Telegraph newspaper that he hoped to work with the former Luxembourg premier to gain a "fair deal" for Britain in Europe.
"If by a fair deal we can agree that we are not heading, at different speeds, to the same place -- as some have assumed up to now -- then there is business we can do," Cameron wrote.
"I do not oppose further integration within the eurozone: I think it is inevitable. Eurozone members must make those decisions.
"But I know the British people want no part of it."
The British premier has said the result could increase the prospects of Britain leaving the 28-member European Union after the referendum on the issue.
But German Finance Minister Wolfgang Schaeuble told the Financial Times that it would be "unimaginable" for Britain to leave, indicating that other EU nations may be willing to offer concessions.
"Historically, politically, democratically, culturally, Great Britain is entirely indispensable for Europe," the minister, who is a one of Chancellor Angela Merkel's closest confidants, said in an interview with the paper published today.
