The three will now work up regeneration plans for the 17-acre Stonegrove and Spur Road estate. Bids are to be submitted in October, although the trio do not expect a selected partner to be named until early next year.
The original tender, advertised in the European Union's Official Journal, said bids must incorporate 200 houses and flats and refurbishment of housing stock.
The estate, built in the 1950s and 1960s, includes seven tower blocks and 587 homes.
Residents' representatives worked with the council on the shortlist. Allan Turner, a Barnet councillor, said that their involvement would help to ensure that the estate was a place where people would choose to live.
Similar schemes are expected for other estates in Barnet, including Dollis Valley and West Hendon.
The architecture partners of the three housing trusts are HTA (Family Housing Association), Hunter & Partners (Metropolitan Housing Trust) and John Thompson & Partners (Guinness Trust).