Shareholders voted 74% in favour of accepting the venture capitalist and supporter's offer of a £5m investment.
The resolution means that Doughty now controls the First Division club and will take over from Eric Barnes as chairman.
When the deal is completed, Doughty will own 85% of the club with the plc owning the remaining 15%.
Forest are reportedly saddled with a debt of £20m and are likely to be one of the club's most affected by the collapse of ITV Digital.
The club have paid the price for their failure to win a quick return back to the Premiership after relegation in 1999.
As a result, their so-called parachute payment, which softens the blow of relegation, ran out leaving them paying players on contracts they could not afford.
This season has seen manager Paul Hart being forced to sell prize asset Jermaine Jenas to Newcastle for £5m and let striker Stern John join Birmingham cheaply.
Doughty's successful rescue bid means that the threat of insolvency procedures against the club has receded.