The new funding, which will kick in from 2021 when the current school building programme ends, will benefit around 50,000 pupils.
New investment models to support the scheme will be developed in partnership with COSLA - the voice of local government in Scotland - and councils. Decisions on which schools will benefit will be focused on those in the poorest condition.
It is expected that design and development work will begin next year.
Swinney said: "Every pupil should have the best support throughout their education, which includes access to high-quality, up-to-date facilities that parents, staff and children can be proud of. This further £1 billion investment will build on the progress already made by the existing Schools for the Future Programme and drive further improvements in the learning estate from 2021.
"We have worked closely with local authorities since 2009 and will deliver 117 new school projects benefitting 60,000 pupils by March 2020. We will keep up the momentum of improvements in education facilities throughout Scotland."
A total of £1.8bn has been invested in the school estate since 2009 through the Schools for the Future programme, comprising £1.13bn of Scottish Government funding and £665m from councils.
A new school project is being delivered in every local authority area in Scotland. The current phase of the programme concludes in 2020.