The DKK 8 billion (EUR 1.1 billion) investment in the world's largest offshore wind developer was given the nod by the Danish Parliament's Finance Committee.
This latest step means that all the necessary regulatory hurdles have now been cleared.
The confirmation of the deal has led to a rupture in the three-party government, with the Socialist People's Party resigning its position in the coalition, stripping it of its majority and plunging the government into crisis.
The banking giant will now hold a 19% stake in Dong. The deal also includes investment from Danish pension firms ATP and PFA to the sum of DKK 3 billion for a 7% stake.
Controversially, Goldman Sachs has been given veto powers under the deal, something which other shareholders are not afforded. Dong will not be able to make acquisitions, issue new shares or appoint a new chief executive or finance director without the bank's say so.
Some in the wind industry have raised fears that such a buy-in from an investment bank could undermine the company's commitment to renewable energy and its move away from tradition energies such as oil.
This was a sentiment echoed by former Social Democrat prime minister Poul Nyrup Rasmussen who told the Politiken newspaper: "Denmark risks losing its leading green position in the world. It almost physically hurts me to see what's going on."
Goldman Sachs was keen to dismiss this notion, saying: "This is a long-term commitment which reflects our support for the management team's current strategy across the company's activities, including the significant renewable energy investments, which we believe will create value for all stakeholders."
According to a leaked document seen by the Copenhagen Post, the Goldman deal was not the highest offer on the table.
Despite what the government had previously claimed, pension fund PensionDanmark's bid for partial ownership of the state-owned energy company was higher than the bid Goldman Sachs offered, the paper claimed.
However, some point to Dong's moves towards a listing on the stock market as justification for the investment. After a failed floatation in 2008, the bank's involvement is seen as increasing the attractiveness of the company in the eyes of potential investors.
Dong said that it expects that the agreement to be implemented at an extraordinary general meeting planned for February 2014.