Detailed proposals for the Edinburgh and South East Scotland city region deal were submitted to the Westminster and Scottish governments in September.
It was put together by six local authorities – Edinburgh, East Lothian, Midlothian, West Lothian, Scottish Borders and Fife.
The hope is to secure £1bn of funding from the UK and Scottish governments and then attract £3.2bn private sector cash to boost the economy by investing in the area’s unique strengths and tackling inequality.
Glasgow secured Scotland’s first City Deal, which was signed last year.
City leader Councillor Andrew Burns said: “This commitment from Westminster is a step forward for our proposals to tackle inequality and accelerate substantial economic growth.”
Mr Osborne said the UK Government was “delivering the most radical devolution of power in British history”.
Mr Osborne said: “We are devolving power to our nations. The Scottish Secretary and I have agreed the new fiscal framework with the Scottish Government.
“We are also opening negotiations on a city deal with Edinburgh, we backed the V&A Museum in Dundee, and in response to the powerful case made by Ruth Davidson we are providing new community facilities for local people in Helensburgh and the Royal Navy personnel in nearby Faslane, paid for by Libor fines.”