The agreed price is £1,662m.
The estate sold comprises some 57,400 married quarters, of which some 2,400 are immediately surplus and will pass to Annington freehold.
The remainder will be leased back by the Ministry.
Annington will draw on the property management expertise of AMEC. The bulk of funding for the acquisition will be provided by Abbey National Treasury Services, Hambros Bank, the Midland Bank, and the Royal Bank of Scotland.
Nomura International is underwriting the whole transaction, and will hold the majority of the risk capital of Annington.
James Arbuthnot, minister of state for defence procurement, said: 'I am delighted with this outcome. We have been working hard for a number of years to put right the problems with service housing, and today's agreement establishes the right foundation for the future.
'We have secured a very good price for the tax payer in a highly competitive auction - and service families will start to see the benefits as a massive programme of housing improvement, made possible by the sale, comes on stream. The new arrangements give us the flexibility we need to tackle the problem of empty MOD homes, and concentrate on the quarters we need, not the ones we don't.
'Ministers have made plain all along that concluding the sale depended on achieving a deal which satisfied the interests of the Services, and a price which properly reflected the public interest.
'Today's agreement does both. The position of the services and residents is fully protected by the legal documentation, and we are confident that we can look forward to a constructive partnership based on Annington's full understanding of Service interests and concerns.
'Like the government, Annington appreciates the vital importance of good housing, and in particular 'patch life', to Service welfare and morale.
'As part of the contract, one of the elements of the deal which had been proposed has been dropped. The Site Exchange Option has been eliminated for the first 25 years. That will reassure those who were anxious about that element of the proposed change of ownership.
'In addition, Annington has undertaken to provide a number of schemes to assist service personnel into home ownership, by offering attractively-priced mortgages and discounted prices on former MOD quarters released to Annington. It will also establish the Annington Trust, a charitable foundation (with start-up capital of some £430,000) to benefit Service families.
'All in all, we have secured a good deal - one that will work to the benefit of the Services, the Ministry and the wider economy.'