In his speech setting out the government's budget plans to MPs, Mr Hammond told the House of Commons that ministers recognised challenges facing the health service.
He pledged an extra £2.8bn in resource funding over the rest of the current financial year and the following two. Documents published by the government setting out the budget plans in full suggest a further £3.5bn capital investment will be made available to back sustainability and transformation programmes (STPs), bailouts for failing trusts and new 'efficiency programmes'.
Of the £2.8bn resource funding, £350m will be made available now to support trusts dealing with winter pressures, the chancellor said, amid predictions that the NHS will face an even tougher winter this year than last.
A further £1.6bn will be added to the NHS budget for 2018/19, with the remaining £850m added to existing spending planned for 2019/20, he told parliament.
The rise falls short of the additional funding demanded by both health unions and the chief executive of NHS England in recent weeks.
The chancellor told MPs that it was 'central to this government's vision that everyone has access to an NHS free at the point of need', calling the health service one of the UK's 'great institutions'.
He said the health service was treating record numbers of patients, had achieved record levels of cancer survival, and highlighted the government's expansion of GP extended hours to offer evening and weekend appointments to 17m patients.
Support for the NHS Five Year Forward View in 2014 reflected the government's backing for the NHS, Mr Hammond told MPs, but he admitted it had not gone far enough.
'Even with this additional funding we acknowledge that the service remains under pressure,' the chancellor said. 'Today we respond. We will deliver an additional £10bn package of investment in frontline services over the course of this parliament.
'To support the STPs which will make our NHS more resilient. Investing for an NHS fit for the future. But we also recognise that our NHS is under pressure right now.
'I am therefore exceptionally - and outside the spending review process - making an additional £2.8bn in resource funding available to the NHS in England. £350m immediately to allow trusts to plan for this winter, £1.6bn in 2018/19, with the balance to come in 2019/20.'
Mr Hammond said the plans meant NHS funding would rise by £3.75bn in total in 2018/19, and deliver a £7.5bn increase to the NHS resource budget over 2017/18 and 2018/19.
The chancellor also pledged to find new funding from outside the existing NHS budget to pay for a new pay deal for nurses if it could be agreed between health secretary Jeremy Hunt and health unions.
Mr Hunt appeared pleased with the extra funding announced by the chancellor, nodding vigorously as the additional funding was unveiled.
The funding rise falls short of demands set out by the BMA earlier this week. Doctors' leaders have called for more than 10% of GDP to be spent on the NHS, to bring the UK in line with other major European nations.
Existing funding plans under the GP Forward View will leave general practice underfunded by £3.4bn by 2020/21, the GPC has warned.
Reacting to the budget announcement, BMA chair Dr Chaand Nagpaul said UK health spending was more than £10bn behind other EU countries and called the budget a 'missed opportunity to put patient care first, address the funding gap and undo damaging cuts to the NHS'.
He highlighted the slump in GP numbers revealed in official data this week, adding: 'With workloads rising and doctors’ pay having fallen by 22% over the last decade, staff morale is low and recruitment and retention is a key challenge for the NHS, yet the budget has offered no solution to this crisis.'