The new funding starts in April 2014 under the 21st Century Schools Capital Funding Programme.
Approval follows the submission of local authorities’ outline programmes of investment last month.
Education minister Leighton Andrews said: “This announcement of nearly £1.4bn over seven years will ensure that we continue to provide the best learning environments for our pupils - helping us to drive up standards across our schools and meet the changing needs of learners.
“Securing capital investment in these difficult economic times is essential, not only for better education outcomes, but for the continued support of our construction industry and the growth of our economy.
“We will now work together with our partners in local government to take this programme forwards and deliver the first wave of a long-term programme of investment.”
The 21st Century Schools Programme has been developed in partnership between the Welsh Government, Welsh Local Government Association, Society of Local Authority Chief Executives and Senior Managers’, Association of Directors of Education in Wales, Diocesan Directors of the Voluntary Aided Sector and Colleges Wales.
Initially the councils only had to find 30% of the funding. Now they will have to match the Welsh government funding, 50/50. The funding is also less than the £4bn that was previously expected for just three years from 2012.
WLGA education spokesman Peter Fox said: “Despite the very difficult funding situation, the joint approach to developing this programme has paid off. Local authorities have prioritised vitally important school building projects in their areas and the funding announced by the minister will enable them to deliver on these priorities.”