Acceptance of the 180p per share deal by independent directors came days after the mega-merger of Beazer and Bryant in mid-December to form the second largest firm in the sector.
Analysts said the Fairview buyout team, led by chairman Dennis Cope, had secured an excellent deal.
One analyst said: "Cope is a very sharp operator. The institutions didn't have much choice. The management was reluctant to go into the public arena in the first place and how can you extract value with a reluctant chief executive?"
An earlier 175p per share management bid for Fairview was rejected as too low by independent directors in November. The new offer values the firm at £307m and is backed by venture capitalist 3i.
Meanwhile, Beazer and Bryant have formed a holding company called Domus out of their merger. The combined group will have a market value of £760m. Its turnover of £1.5bn will make it second only to Barratt in size. Three hundred jobs will be lost as a result of the deal.
Beazer chief executive John Low will be chief executive of Domus, Bryant chief executive Peter Long becomes deputy chief executive, Bryant finance director Patrick Scannell becomes finance director and Bryant chairman Hubert Reid will act as chairman. Former Beazer chairman Victor Benjamin has retired.
Domus chief executive John Low said each firm would bring strengths to the new company. He said: "We had both been looking at opportunities. This is a merger of equals. They are both very strong household names.
"Size isn't important; it's about a real opportunity to provide a broad-based housebuilding business. A merger is a new outlook."
Low said the deal could spark further consolidation in the housebuilding sector.
"There has been a massive amount of talk in the sector over the last two years; I wonder whether people will look at how well received we have been and see how they could be taken forward."
Low added that the job losses would largely be in administrative areas where the merger would result in an overlap of staff. The Beazer, Bryant and Charles Church brands will remain in place.
n Housebuilder and developer Country & Metropolitan Group has released preliminary figures for the year ended 31 August that show a record profit of £1.6m, a rise of 60%, from a turnover that fell 13% to £16.2m from £18.7m.