Mr Osborne unveiled the deal in his Autumn Statement and said the city would be given the status to invest in infrastructure.
Glasgow and other Clyde Valley councils will get access to City Deal, an initiative previously available only in England. Under the scheme the city will negotiate deals with the Government - deals that give Glasgow new powers in exchange for greater responsibility to stimulate and support economic growth in the area.
The scheme means cash invested by councils is "earned back" through income tax, corporation tax, VAT and PAYE contributions.
Mr Osborne said: "The Government is working with Glasgow City Council to support delivery of Glasgow's vision for a City Deal, which will help make Glasgow one of the fastest growing city regions in the UK."
The details have still to be agreed but the move was welcomed by the council.
Council leader Gordon Matheson said it was a "massive boost". He added: "We very much welcome the Autumn Statement announcement. We have been working on this for some time with the UK Government and councils across the Clyde Valley.
"We will agree the fine details with the UK and Scottish Governments, but the reference in the Autumn Statement is a massive boost."
Stuart Patrick, chief executive of Glasgow Chamber Of Commerce said: "We endorse the principle of a City Deal on two counts.
"Firstly, because it will involve substantial investment in the economic infrastructure of our city, and, secondly, because the firm discipline involved in agreeing the projects gives the local authorities a clear incentive to choose projects that have the biggest impact on economic growth."
As well as Glasgow, the areas to benefit from the City Deal include North Lanarkshire, East Renfrewshire, Renfrewshire, East Dunbartonshire, South Lanarkshire, West Dunbartonshire and Inverclyde.
The Scottish Government's budget will increase by £308million over the next two years, the Chancellor said, but he came under fire for other announcements in his Statement.
He said the state pension age would increase to 68 in the mid-2030s and to 69 in the late 2040s.
Next April, the state pension will rise by £2.95 a week, but overall welfare spending is to be capped.
Scottish Finance Secretary John Swinney said: "Under Westminster plans, people in Scotland will enjoy fewer years of retirement than people in almost any other country in western Europe.
"The increase in the pension age will specifically hurt people on lower incomes who, unfortunately, have lower life expectancy and fewer alternatives to the state pension."
John Dickie, head of the Child Poverty Action Group in Scotland, said: "The Chancellor has failed to take the action needed to reverse the explosion in child poverty forecast across Scotland and the rest of the UK.