The Prime Minister said the City Deals fund would create tens of thousands of jobs, fund transport projects, boost sectors like life sciences and resurrect the scrapped Glasgow Airport Rail Link scheme.
In a joint statement with Chief Treasury Secretary Danny Alexander, Mr Cameron also challenged the Scottish Government to match the cash, which the SNP administration later said it would.
Mr Cameron said: "This shows how Glasgow can benefit from having the best of both worlds - a devolved Government in Scotland and the broad shoulders of the UK Government that can use its influence and resources to unlock vital investment."
But Deputy First Minister Nicola Sturgeon said the Scottish Government had already invested £1.5 billion in major Glasgow projects including a new hospital, transport schemes and the Commonwealth Games, which begins later this month.
She added: "Today's announcement shows that the referendum has made the UK Government sit up and take notice of Scotland."
In his Autumn Statement last year, Chancellor George Osborne announced Glasgow would be the first city in Scotland to benefit from City Deal status, an agreement between the UK Treasury and a city region. Such deals are already in place in Manchester, Leeds and Liverpool.
The UK Government yesterday put a figure on that promise, claiming the investment could create 28,000 new jobs over the next 20 years and eventually generate about £1.75bn of economic growth in the city every year.
The City Deal has been developed by officers from the eight participating councils in the Clyde Valley, which will contribute a combined £130 million. Westminster also said the fund would provide targeted support to more than 4000 disabled people in work or looking for work and 15,000 young people over the next three years.
Glasgow will be expected to respond by taking active measures to further reduce unemployment and help move people in low-paid jobs into higher-paid ones.
Milestones will be negotiated with HM Treasury, while the participating authorities will need to agree to a phased and prioritised programme of investment and about how the schemes will have an impact.
The joint statement said: "These are genuine powers that will change the fortunes of people across the region by creating new jobs, improving transport networks, boosting businesses and providing skills to young people and the long-term unemployed."
But Ms Sturgeon claimed the scheme amounted to £15m a year for the first five years, with future years' funding contingent on a review, while claiming it was "regrettable" other Scots cities were not included.
She added: "The UK's proposed £15m a year is dwarfed by the Scottish Government's ongoing investment in Glasgow. Investment in the Commonwealth Games, the new Southern General hospital, Fastlink and the Glasgow Subway improvements alone amounts to a massive £1.5bn in capital spend."
Councillor Gordon Matheson, Leader of Glasgow City Council, said: "This is fantastic news for Glasgow and the Clyde Valley. It will help us to move to the next level in terms of economic growth for the City Region.
"We have been working closely with the UK Government on this project for some time, and I am delighted to say it has borne fruit.
"The City Deal will bring tens of thousands of jobs, encourage growth and improve our competitiveness to bring benefits across the whole of the Clyde Valley area for the next 20 years."