Nearly 733,000 premises in Wales have been connected to fibre broadband as a result of the Superfast Cymru scheme.
Some 717,000 of these can achieve speeds of 30Mbps or more, while the remainder can get speeds of at least 24Mbps.
The Superfast Cymru project saw the Welsh government enter into a partnership with Openreach, the European Regional Development Fund and the Westminster government.
According to Julie James AM, Leader of the House with Responsibility for Digital, the scheme has "undoubtedly been a success and has delivered a real step change in the availability of superfast broadband across the whole country".
"Of all those with access in Wales, over half are as a result of our intervention," Ms James commented.
"That in itself shows the positive impact this programme has had."
Ms James noted that without Superfast Cymru, entire local authority areas would have been "untouched" by superfast broadband.
However, she said there is now not a single local authority area without access, with even remote locations boasting some of the highest speeds in the UK.
Ms James went on to note that while Superfast Cymru has "successfully changed the digital landscape in Wales", she remains very aware that some premises still do not have access to superfast broadband connections.
"We are now working on how to reach these," she stated.
Kim Mears, Managing Director of Openreach, added that the scheme was an "enormous engineering project, with a complex set of challenges".
However, she said its engineers have "risen to the task, delivering one of the outstanding digital network rollouts in Europe".
"We’re very proud of what we’ve delivered in Wales," Ms Mears commented.
"Building fast and reliable broadband infrastructure is another step towards Wales becoming a truly united and connected nation."
Ms Sears stated that Wales can now "confidently claim" to have better superfast broadband coverage than Germany, France, Spain and Italy.
Nevertheless, she stressed that Openreach remains mindful that some communities are still waiting to gain access to better connections.
"We’re more determined than any other business to reach these remaining areas," Ms Mears insisted.
"We’re also committed to exploring the alternatives with the Welsh government to make decent broadband a reality for all."