The prime minister said contributions will rise “a bit”, but delayed further details until the autumn budget.
She promised the contributions would be calculated in a “fair and balanced way”.
Most think Brexit dividend pledge ‘dishonest’ – poll
Speaking at the Royal Free Hospital in north London, Mrs May also repeated her claim that a “Brexit dividend” would help foot the bill.
Critics say the “dividend” will simply not exist, with Conservative MP and former GP Sarah Wollaston describing the idea as “tosh”.
Announcing the funding boost, Mrs May said: “We cannot continue to put a sticking plaster on the NHS budget each year.
“So we will do more than simply give the NHS a one-off injection of cash…
“This must be a plan that ensures every penny is well spent.
“It must be a plan that tackles wastes, reduces bureaucracy, and eliminates unacceptable variation, with all these efficiency savings reinvested back into patient care.”
Asked by Sky News when patients could expect to see improvements in NHS care, the prime minister did not give a timeframe.
She said she wanted to see better mental health services and cancer survival rates.
On who would be hit by more tax rises, Mrs May pledged she would “listen to views about how we do this”.
Amid speculation as to how the funding boost will paid for, the Financial Times reports that the PM has given Chancellor Philip Hammond a “free hand” in figuring out how to fund it, telling him “nothing is off the table”.
Meanwhile, The Times reports that Mr Hammond has ruled out extra spending in areas like schools, defence, prisons and police as a result of the cash injection for the NHS.
Speaking in the Commons following the PM’s speech, health secretary Jeremy Hunt said a “putting the economy back on its feet dividend” would help fund the boost for the NHS, alongside a so-called “Brexit dividend”.
He also insisted the government was able to announce the funding injection not only due to the “Brexit dividend”, but also a “deficit reduction dividend” and a “jobs dividend”.
Mr Hunt said the announcement was “bold and ambitious”, adding: “Some of the new investment in the NHS will be paid for by us no longer having to send annual membership subscriptions to the EU after we have left.
“But the commitment the government is making goes further and we will all need to make a greater contribution through the tax system in a way that is fair and balanced.”
Jonathan Ashworth, Labour’s shadow health secretary, said the money was “not enough to save our NHS” after eight years of austerity.
“People are waiting longer and in pain because of Tory cuts to the NHS,” he said.