It will succeed the £425m Superfast Cymru project, which aims to reach 96% of premises by the end of 2017.
Ministers hope to get £20m in EU aid, and raise £37m by investing their share of BT's profits from new customers.
Skills and Science Minister Julie James said: "We know there is more to do ... to bring faster broadband to those final hard-to-reach areas."
Welsh Conservative economy spokesman Russell George welcomed the announcement, after AMs criticised the roll-out in a Tory-led Senedd debate on Wednesday.
"Recent history reveals a record of over-promising and under-delivering," he said.
"Many communities are either still waiting for access or have not been incentivised to use a service that's now available to them.
"It's vital that lessons are learned, and that this money is used effectively to improve broadband connectivity across Wales."
During the debate, Plaid Cymru AM Dai Lloyd criticised the take-up rate, saying fewer than a third of premises capable of receiving the service had signed up for it.
Up to £80m will be spent to ensure every property in Wales can access superfast broadband in a new scheme.