The council's executive board agreed a short-term loan, believed to be about £400,000, to support a takeover bid to take the club out of administration.
The consortium is hoping to finalise the £3.3m deal shortly.
The authority said it would work closely at helping secure the long-term viability of Wrexham's Racecourse stadium.
The consortium is led by Wrexham car dealer Neville Dickens and Chester travel agent Geoff Moss.
Council leader Aled Roberts said: "The council will now work closely with the prospective purchasers and will be working with partner organisations to secure long term viability for the Racecourse ground as a regional stadium."
Expulsion
The council said the terms of the loan must remain confidential but it had "taken a strictly commercial view in coming to this decision".
Councillors have already granted outline planning permission for the consortium to go ahead with a multimillion-pound redevelopment around the edge of the stadium.
The scheme includes an eight storey block of flats for 300 students at the nearby North East Wales Institute, together with private apartments, a retail area and a new stand.
Earlier this month the Football League voted to accept the consortium's rescue plan and allow more time for the deal to be completed so that the Dragons can continue to play in League Two next season.
The league's original deadline for Wrexham to be taken out of administration or face expulsion expired on 3 June, but a spokesman said the board recognised that formalities had to be completed before Mr Dickens' consortium could finalise the takeover.
Last month, creditors of the club, which went into administration in December 2004 with debts of £4.7m, voted to accept a dividend of at least 27.7p in the pound.
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