South Northamptonshire Council's planning committee last night approved two outline applications for the scheme, which would also provide a primary school and a new local centre.
The plans by housebuilder Bloor Homes for a site at Upper Harlestone, were last week also approved by members of Daventry District Council, since the proposed development covers land in both districts.
A report by Daventry planning officers said the development "will deliver a balanced and sustainable development of up to 1,750 new homes and community infrastructure in an attractive, [well-designed], landscaped and pleasant environment".
Both councils said the 83 hectare scheme was acceptable because it sits within a site allocated for 2,550 dwellings within the West Northamptonshire joint core strategy, adopted in December 2014.
The joint plan covers Daventry district, Northampton borough and South Northamptonshire district council areas.
Daventry planners said the council cannot currently demonstrate a five-year supply of housing.
Their report said "the need to bring forward development that can be delivered in the short term is emphasised to avoid additional pressure for opportunistic 'windfall' development on sites much less sustainable".
It added: "This is a significant material consideration in favour of the proposed development and must be weighed as part of the planning balance exercise."
Two affected parish councils lodged objections to the planning applications due to concerns over the amount of traffic that would be generated.
However, the Daventry planning report said the traffic impacts could be mitigated through a section 106 agreement and relevant planning conditions.
Following a viability study, the council has agreed to a level of 26 per cent affordable housing on the development, rather than the 35 per cent required by policy at both councils.
The Daventry planning report advised that planners "considered that the development of the site can make appropriate contributions to community infrastructure and affordable housing whilst still returning a reasonable return."
The South Northants officer's report said that the scheme would take up agricultural land and change the appearance of the area.
But it said that, on balance, that change is justified "by the positive contributions that the scheme will make" and because the changes were already considered when the site was allocated in the joint core strategy.
The report added that the council "accepts that it cannot currently demonstrate that it has a five year housing land supply" and "recognises the contribution towards affordable housing provision and substantial contribution towards meeting the housing needs ... as a material consideration in favour of the proposal".
In April, councillors in Northampton endorsed a draft local plan that proposes allocating 81 new sites for 4,750 homes and stepping up housing delivery levels to tackle a shortfall against adopted joint core strategy targets.