The Cardiff Capital Region City Deal will see £734m invested in the Metro transport scheme and £495m in other projects.
Vale of Glamorgan council became the final authority to back the deal on Thursday.
Ten councils will formally sign up to the deal on 1 March.
Blaenau Gwent, Bridgend, Caerphilly, Cardiff, Merthyr Tydfil, Monmouthshire, Newport, Rhondda Cynon Taf, Torfaen, had already backed the deal.
The local authorities - which have committed to contribute a total of £120m - will be "locked in" to the deal for five years before any can quit.
Vale of Glamorgan council leader Neil Moore said the city deal would bring economic and social benefits to the area.
"I now look forward to working with colleagues across the region to deliver the objectives of the compact between the ten councils, Welsh Government and the UK government."
A £1.2bn deal to boost economic growth in south east Wales has got a step closer after being backed by all ten councils.