Drainage work on land between junction 12, Tal-y-Bont, and junction 13, Abergwyngregyn, will begin in the autumn, once the landowners agree.
It is part of a stretch of the A55 closed by flooding on Boxing Day.
First Minster Carwyn Jones also said a separate £1.9m Tal-y-Bont scheme is due to start in the spring and be ready for winter.
Mr Jones visited the village, also hit by flooding over Christmas, in January - a week after residents complained they had been left waiting for him after he had driven through the village without stopping.
He apologised but said he did not know they had been expecting him.
Visiting the Traffic Management Centre in Conwy on Thursday, he said: "When I saw the flooding on the A55 and then met residents of Tal-y-Bont who had been affected, I said that the money was available for a flood alleviation scheme to help reduce the risk of it happening again.
"Following discussion with Gwynedd council, I'm pleased to say that construction can start this April and will be complete ahead of next winter."
He said the A55 work "needs a great deal of planning because of its sheer scale".
"The plan is not that there are perpetual road works on the A55," he added.
"At the moment, we need to make sure that the tunnels are safe for the future.
"We're not planning any works after Easter of this year, but you have to remember that the A55 was built on the cheap, unfortunately.
"If you look at some of the sections like the tunnels, it's just the old road. We would never build a road like that now, we would build a far better road. So we have to improve the road's resilience for the future."
A £500,000 grant to speed up flood prevention work on the A55 in Gwynedd has been announced.