Energy minister Amber Rudd gave the commitment at a speech in London.
"Today I can announce that – if, and only if, the government's conditions on cost reduction are met – we will make funding available for three auctions in this parliament," Rudd said. This first auction is expected in 2016.
"The industry tells us they can meet that challenge, and we will hold them to it. If they don't there will be no subsidy. No more blank cheques," she added.
Rudd also said up to 10GW of new offshore projects could be supported in the 2020s.
RenewableUK deputy chief executive Maf Smith said the announcement would boost investor confidence: "Today's speech provides clarity on where the government stands on the future of offshore wind, which will give developers the confidence to invest in the British economy.
"Industry has already shown it can rise to the challenge of reducing costs and offshore wind companies are confident they will be cost competitive with new gas and new nuclear by 2025," he said.
The CfD subsidy is replacing the renewables obligation certificate support scheme. CfDs guarantee a set price for the electricity produced – known as a strike price.
A first round of auctions for CfDs were awarded in February 2015. Two offshore projects won support - ScottishPower Renewables' 714MW East Anglia One and Mainstream Renewable Power's 448MW Neart Na Gaiothe. The average price of the agreed strike price was £117.14 (€167/MWh).
In April 2014, five offshore projects were awarded final investment enabling CfDs, at £140/MWh for the majority of the 15-year contracts.
There was no mention of support for onshore wind. The current UK government is setting out its plan to end onshore subsidy for new projects by closing the renewables obligations system earlier than expected. It also believed onshore wind will not be eligible for future CfD auctions.
Rudd's speech also laid out plans to close all coal power stations in the UK by 2025 and restrict their use from 2023.