It hailed the £425m deal as the biggest of its kind in the UK and a boost for the economy.
Mr Jones said: "Today is the day that Wales moved into the fast lane."
It will mean broadband speeds for Wales around 15 times faster than those available now.
According to a report out this week by the regulator Ofcom, Wales has the lowest level of super fast broadband in the UK, with 34%.
Most of the improvement will be in towns and cities where the density of the population means the private sector can provide the infrastructure at a profit.
Coverage in Scotland is 42% and in Northern Ireland, where there has already been a big push, is 96%.
The £425m next generation broadband scheme for Wales, about half of which will be paid for by the public sector, will lay fibre optic cables across tens of thousands of miles.
The announcement on Thursday, made at the first minister's end-of-term news conference, follows an 18-month procurement process.
The Welsh government asked the industry what plans businesses had to invest in the network.
Officials say 52% of Wales would not have benefited from next generation broadband without government intervention.
BT was the only company left in the process after the last of the others pulled out earlier this year.
But Mr Jones insisted the deal was good value for the taxpayer, with every £1 of Welsh government investment matched by £6 from other sources.
The Welsh government is spending some £58m on the scheme, with a similar amount coming as a result of UK government spending and £90m of European funding.
'Overtake' The agreement is subject to state aid approval from the European Commission.
Mr Jones said: "Our partnership with BT will see to it that Wales does more than simply catch with our neighbours.
"We intend to catch-up, overtake and then set the pace that others will strive to match."
BT Openreach chief executive officer Liv Garfield said the company's vans would soon be on the road as part of a "huge physical engineering journey".
Download speeds of up to 80 megabits per second (MBS) will be offered, compared to the average download speed currently available in Wales of about five to six MBS.
Even faster connections of up to 330MBS will be available to businesses who want it in some parts of Wales.
BT will create 50 jobs and 100 apprenticeships. Another 320 existing jobs will be protected.
It will also offer work experience to 900 young people as part of an agreement that was welcomed by the Communication Workers' Union.
Welcoming the announcement, Wales Office Minister, David Jones said: "By having access to ultrafast broadband, businesses can expand, develop new markets, create the jobs we need and compete with others around the world.
"It also allows local communities in the most rural areas of Wales to access public services more quickly and efficiently online.
"This announcement today will help ensure that businesses in even the most rural parts of Wales can continue to thrive."
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