The report by economic consultancy Volterra Partners, which was commissioned by mayoral agency Transport for London (TfL) for the London boroughs of Wandsworth and Lambeth, anticipated the project could create between £1.6 billion and £7.9 billion in growth.
It said the economic benefits of building two new tube stations, at Nine Elms and Battersea, would pay for the scheme between three and nine times over.
According to the report, the Northern Line Extension (NLE) would enable the underdeveloped Nine Elms district to support the same high levels of commercial activity as the rest of central London.
The London Borough of Wandsworth wants to transform the 180-hectare Nine Elms, a site on the South Bank into a high-density residential and business quarter.
According to the council, a regenerated Nine Elms could provide up to 25,000 new jobs, 16,000 new homes and will include the new US Embassy and a revamped New Covent Garden Market.
Volterra chair Bridget Rosewell said: "Nine Elms sits within the most productive commercial territory in the UK.
"The Northern Line Extension will unlock its clear potential as an international business district with a high level of employment density."
As well as the tube link providing the necessary transport capacity for Nine Elms, she also said it would "expand the engine room of the UK economy".
The report’s findings will be included in a planning application for the extension being prepared by TfL.
The application could be submitted in early 2013, subject to financing arrangements, and, if approved, the new tube stations could open by 2018, Wandsworth said in a statement
The GLA wants the Nine Elms site to become an enterprise zone, which it hopes will be finalised by next month’s budget.
But speaking at a media briefing this week, London mayor Boris Johnson's chief of staff, Sir Edward Lister, said that the enterprise zone would not have a fast-track planning process because "massive" applications are involved, which he said would need full consideration.
Lister said: "In that sense, the enterprise zone is not exactly perfect for what we are trying to do, to fund infrastructure now."
Lister said that the GLA was seeking powers to finance the Northern Line extension using Tax Increment Financing (TIF).
TIF allows local authorities to borrow against the future growth of business rates in an area over a 25-year period to pay for infrastructure at an early stage of a project.
In last year's Autumn Statement, chancellor George Osborne revealed that the project to extend the Northern Line could become the first scheme in the country to benefit from powers allowing borrowing against expected future receipts from the Community Infrastructure Levy.
The Nine Elms regeneration area received a boost last night when Wandsworth Council approved plans for the six-hectare Embassy Gardens development.
This will provide 2,000 new homes with shops, cafes, bars, restaurants, business space, a 100-bed hotel, health centre, children’s playgrounds and sports pitches, plus about 2.5 hectares of outdoor public space.