The company, which trades from about 40 offices in and around London, plans to raise £55 million through an offer of new shares in a flotation expected to value it between £400 million and £500 million.
Private equity owner BC Partners will sell some of its stake, while directors are also expected to earn a windfall of up to £100 million.
Foxtons is capitalising on a buoyant London market, inflated by demand from cash rich foreign buyers and Government stimulus schemes such as Help to Buy.
A successful flotation would mark a substantial turnaround in fortunes for BC Partners, which also owns mobile phone retailer Phones4U.
BC Partners bought Foxtons for about £375 million at the peak of the market in May 2007 from founder Jon Hunt, just months before the credit crunch sent house prices plunging - a purchase it described as a "mistake".
The company was taken over by its lenders in 2010 in a deal which slashed its debt, before the private equity firm regained control last year.
Foxtons, known for its distinctive fleet of Mini Coopers, typically sells properties for between £200,000 and £1.4 million in upmarket parts of the capital.
About 44% of its revenues come from home sales, while 53% are from lettings.
It made underlying earnings of £38.3 million last year on revenues of £120 million. Underlying profits in the first six months of this year were up 14.3% on a year earlier to £19.4 million, while revenues rose 10.5% to £62.6 million.
Foxtons said it is well placed to benefit from any improvement in the housing market.
It said: "The limited geographical area of London (and in particular its prime residential areas), combined with low levels of house building in London and planning restrictions on new building or redevelopment of property, have led to a constraint on the supply of residential properties in London and created excess demand which has resulted in resilient prices."
Foxtons plans to open five to 10 new branches a year between 2014 and 2018, and could also expand in the South East in the longer term.
Its first branch opened in 1982, and by 2001 it had 10 branches. It now has 40 offices in London and two in Surrey.
The housing market has been given a boost in recent months by Government schemes such as Help to Buy, which offers loans to allow people to buy new-build homes with a deposit of just 5%.
Foxtons expects to float on the stock market next month, after which around half of its shares will be in public hands.
Directors, including boss Michael Brown, are expected to earn a multi-million pound windfall by selling some of their reported 20% stake. It will also raise about £55 million through a placing of new shares to wipe out debt.
Foxtons also has a mortgage broking business Alexander Hall, which offers independent mortgage advice.
The UK's biggest estate agency chain Countrywide also rejoined the stock market earlier this year, valued at more than £800 million.
The group, which has almost 1,000 branches, trades through brands including Bairstow Eves, Gascoigne-Pees and Hamptons International.