Voters in the village were 97 per cent in favour of the purchase. If the project goes ahead, it will result in Scotland's first commercial community-owned building.
The acquisition makes use of a Scottish law, passed in 2003, that allows rural communities to have priority over other buyers if they declare their interest before a building goes on the market.
The project is being managed by the Neilston Development Trust, which must now submit a proposal to the Scottish Executive for permission to buy before applying for funding from the Big Lottery Fund's Growing Community Assets fund.
The property has been valued at £210,000, but the overall cost of the project could be several times that amount because of the need to pay for conversion work and staff salaries.
The Neilston community facility will function using the same model as a social enterprise, with any profits being reinvested in the organisation.
Community Enterprise in Strathclyde, a local support organisation, will help to formulate a detailed business plan once permission to buy has been obtained.
Pauline Gallacher, project co-ordinator at the Neilston Development Trust, said the purchase was not simply a matter of village residents trying to prevent commercial development.
"This is an opportunity for a community to own an asset that it can use for local benefit," she said. "We already have a local authority hall, but we don't have a small, family-friendly and flexible space that can be used for meetings."
Gallacher hopes the project will encourage community purchases in other urban areas. "Three other communities in Scotland have bought land under the 2003 Act, but they are smaller and more remote," she said.
The trust has until 25 November to conclude the deal, although the centre will not be in use before the end of 2007 at the earliest. When it does open, East Renfrewshire Credit Union is likely to be one of the property's first anchor tenants.