"It's very much formulated down to the final strokes. We haven't put it in quite yet but we're going to be doing it soon," said Mr Trump.
Republicans have taken the first steps towards dismantling President Barack Obama's signature healthcare law.
But they have yet to rally around an alternative plan.
In an interview with the Washington Post, the president-elect said he was ready to reveal a new bill with congressional leaders.
That would happen when his health secretary pick, Tom Price, was confirmed, he said.
"We're going to have insurance for everybody. There was a philosophy in some circles that if you can't pay for it, you don't get it. That's not going to happen with us."
People covered under the law "can expect to have great health care," he added.
"It will be in a much simplified form. Much less expensive and much better."
Can Obamacare be repealed?
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The Affordable Care Act, known as Obamacare, has provided healthcare subsidies and medical coverage for millions who are not covered through work.
It has banned insurers from refusing coverage to people who are already ill, and curbed medical charges to the sick and elderly.
But the law has been hit by rising premiums, large fees and national insurers exiting the marketplaces.
On Friday, the US Congress took a first step toward dismantling Obamacare.
Republicans in the House passed a budget measure to introduce a bill - which Democrats cannot block - to roll back the law.
The US Senate had already passed the measure, which instructs four committees on Capitol Hill to draft repeal legislation by 27 January.
On Sunday, Democrats staged dozens of rallies across the country to express their opposition.
President-elect Donald Trump has promised "insurance for everyone" as Republicans draw up a replacement for the Affordable Care Act.