Ministers also pledged to spend £370 million on flood defences in 2015/2016, and maintain spending in real terms over the following six years, as part of the £100 billion investment in infrastructure projects announced on Thursday.
The Government hopes the investment will better protect 300,000 more homes by 2021, bringing down the overall risk of flooding and the cost of insurance.
Ministers had been locked in negotiations with the insurance industry over a replacement for the "statement of principles" that runs out at the end of next month, under which insurers continued to provide flood cover for at-risk properties.
However, as the threat of flooding has grown across the UK, premiums and excess payments for homes in high flood risk areas have increased.
The new deal will cap flood insurance premiums, linking them to council tax bands so that people will know how much they have to pay, the Environment Department (Defra) said. A levy paid by household insurers into a fund will be used to pay claims for people at a high risk of flooding.
Environment Secretary Owen Paterson said: "Flooding is terrible for anyone affected by it. We have worked extremely hard with the industry to reach an agreement on the future of flood insurance. There are still areas to work through but this announcement means that people no longer need to live in fear of being uninsurable and that those at most risk can get protection, now and in the future."
Otto Thoresen, the ABI's director general, said: "Insurers' priority has always been to ensure that flood insurance remains affordable and available for everyone who needs it. Today's announcement is the start of a process that aims to deliver affordable flood insurance to high flood risk households." He said getting to this stage had required compromise on both sides, and to establish the "Flood Re" system would take an "unprecedented level of partnership" between the Government and the insurance industry.
Shadow environment secretary Mary Creagh said: "People in areas of high flood risk are being hit now with higher insurance premiums and excesses because incompetent ministers have failed over the last three years to get a deal with the insurance industry. The process announced today is fraught with difficulties and may not be completed by the time of the next election. The Government's proposals raise serious questions about how much all householders will pay into the Flood Re scheme, the affordability of flood insurance and who picks up the bill in the event of a catastrophic flood."